Shift selector WHEN IT IS COLD IT IS HARD TO CHANGE THE SHIFT SELECTOR.

Tiburon (means shark)_ this word, (sp)
hot or cold engine or both
what is engine RPM hot, 800 if over that shifts can be violent. at idle.
cold rpm 1500 are more rough, due to higher RPM, cold controls.

No engine size told << and this tells transmission there.
Well that is transmission (actual) problem
F4A42 ?there are 3 kinds used.
6HP19 and
ZF6HP19 so did you scan the pCM first.? if not why not? what it it told you why?

there is a device in the transmission called an Accumulator
this is shock absorber (real name) and does just that to stop just that.
shock . (and air shock absorber actual)<< deep deep inside it

modern transmissions even control main line pressure.controller
solenoid, called PCS or PCV, that if bad , causes too high line pressure. (there a test port for this and the service manual on this car
tells how to do that test)
the box 2.7L has 5 solenoids,
one is called Damper clutch solenoid valve
My Korean is weak and that is not a common name . F4a42
the books states
If the engine stalls when the selector lever is shifted from N to D or R range while the engine is idling, the cause is probably a malfunction of the engine system, damper clutch solenoid valve, valve body or torque converter (damper clutch malfunction).
N>D shock
If abnormal shocks or a time lag of 2 seconds or more occur when the selector lever is shifted from N to D range while the engine is idling, the cause is probably abnormal underdrive clutch pressure or a malfunction of the underdrive clutch, valve body.
N>R shock

Shocks when changing from N to R and large time lag
If abnormal shocks or a time lag of 2 seconds or more occur when the selector lever is shifted from N to R range while the engine is idling, the cause is probably abnormal reverse clutch pressure or low and reverse brake pressure, or a malfunction of the reverse clutch, low and reverse brake, valve body or idle position switch.

read here.

https://eautorepair.net/Marketing/Default.asp

Have you ever had the transmission serviced? No guarantee, but I bet it will operate fine if you have the filter and fluid changed.

Not hard to replace. But you can't buy them., unless you get the entire steering column. Just did a Ford, same set up. Junk yard part is cheaper.

jack up and safely go under neath vehicle and check the shift selector connection if good check cable /linkage from tranny to selector for proper connections and operations if good --try moving selector if moves try to put in neutral if hard to move or selector wont move possible internal gear damage

This sounds like a shift cable linkage problem to me. Check to make sure the shift linkage is responding properly to the shift selector by having someone shift it while you watch the linkage under the hood. Also make sure there is nothing blocking the selector from moving and the cable is free of kinks and other cables or things pressing on it. Of course do this with the engine off for safety. Also try manually turning the shift selector lever and make sure it is engaging, there should be a nice stiff slick. If the cable and selector are working properly then you might have a bigger transmission issue on your hands.

There are few related help links related to gear shift issues:----
Click the link below:----
Gear indicator Shows "3" Instead Of "D"? http://whoisbyme.blogspot.in/2012/07/gear-indicator-shows-3-instead-of-d.html 2006 Chrysler 300c: Shifter Stuck in Park? http://technoanswers.blogspot.in/2012/06/2006-chrysler-300c-shifter-stuck-in.html 1998 Ford Expedition: Will not Shift Out of Park? http://schematicsdiagram.blogspot.in/2012/06/1998-ford-expedition-will-not-shift-out.html Car will not move when in gear?

http://repairhelpcenter.blogspot.in/2012/02/car-will-not-move-when-in-gear.html Mercedes-Benz transmission sticks in first gear? http://technoanswers.blogspot.com/2012/01/mercedes-benz-transmission-sticks-in.html Mercedes Benz not engaging in first gear? http://technoanswers.blogspot.com/2012/01/mercedes-benz-not-engaging-in-first.html Chrysler PT Cruiser only goes in First gear?

http://howtobyme.blogspot.com/2011/11/chrysler-pt-cruiser-only-goes-in-first.html

Car is stuck in park and the shift will not move?

http://howtobyme.blogspot.com/2011/08/car-is-stuck-in-park-and-shift-will-not.html

2007 Ford Expedition: How to shift car in neutral with Dead Battery http://www.howtorepairguide.com/2012/11/2007-ford-expedition-how-to-shift-car.html 2002 Nissan sentra will not go out of park mode? http://technoanswers.blogspot.in/2012/02/2002-nissan-sentra-will-not-go-out-of.html Nissan Sentra stuck in park? http://technoanswers.blogspot.in/2012/02/nissan-sentra-stuck-in-park.html Car will not come out of Park?

http://howtobyme.blogspot.com/2011/11/car-will-not-come-out-of-park.html

Automatic transmission will not go into high gear?

http://howtobyme.blogspot.com/2011/11/automatic-transmission-will-not-go-into.html

Car won't downshift sometimes?

http://schematicsdiagram.blogspot.com/2011/12/car-wont-downshift-sometimes.html
Buick Park Avenue: Transmission will Not shift into drive?

http://schematicsdiagram.blogspot.com/2011/12/buick-park-avenuetransmission-will.html
No First gear Starts In Second Gear http://www.howtobyme.blogspot.com/2012/07/no-first-gear-starts-in-second-gear.html Ford Taurus won't shift from park? http://schematicsdiagram.blogspot.com/2011/12/ford-taurus-wont-shift-from-park.html 2006 Ford F150: Will Not Shift out Of Park? http://technoanswers.blogspot.in/2012/06/2006-ford-f150-will-not-shift-out-of.html Car Transmission will not go into Park mode?

http://schematicsdiagram.blogspot.com/2011/12/car-transmission-will-no-go-into-park.html
1998 Chrysler Voyager: Transmission Problem? http://howtobyme.blogspot.in/2012/06/1998-chrysler-voyager-transmission.html Shift indicator directly goes to 2nd when key is turned ON?

http://schematicsdiagram.blogspot.com/2011/12/shift-indicator-directly-goes-to-2nd.html
Third gear missing and engine losing power?

http://schematicsdiagram.blogspot.com/2012/01/third-gear-missing-and-engine-losing.html
Chevrolet silverado has whining sound in gear?

http://technoanswers.blogspot.com/2012/01/chevrolet-silverado-has-whining-sound.html
2002 Chevrolet Avalanche Z71: Gear shift Issue? http://whoisbyme.blogspot.in/2012/06/2002-chevrolet-avalanche-z71-gear-shift.html Hard to shift gears on Manual transmission?

http://technoanswers.blogspot.com/2012/01/hard-to-shift-gears-on-manual.html
Car hard shift at slow speeds?

http://technoanswers.blogspot.com/2012/01/car-hard-shift-at-slow-speeds.html
Transmission-Hard To Down Shift http://technoanswers.blogspot.in/2012/07/transmission-hard-to-down-shift.html Automatic transmission shift lever hard to move on cold mornings?

http://technoanswers.blogspot.com/2012/01/automatic-transmission-shift-lever-hard.html
2000 Nissan maxima shifts hard?

http://schematicsdiagram.blogspot.in/2012/02/2000-nissan-maxima-shifts-hard.html
Vehicle noticed sluggish delayed shifts while driving?

http://schematicsdiagram.blogspot.in/2012/03/vehicle-noticed-sluggish-delayed-shifts.html
2007 Hyundai Santa Fe: Will not Shift out of Park Mode? http://schematicsdiagram.blogspot.in/2012/06/2007-hyundai-santa-fe-will-not-shift.html

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These will help.
Thanks.

shifter linkage needs adjustment or something has fallen in to shifter mechanism

heater sounds like the coolant level is low,transmission sounds like a shift solenoid sticking

Some modern vehicles when change the shift pattern while the engine is cold, by keeping the vehicle in a lower gear for a higher rpm while the engine is cold, the engine warms up faster, to reduce emissions. (Emissions are higher while the vehicle is cold)

What you may be experiencing is that the shift from first to second occurs at a higher rpm when the engine is cold than when warm. This can lead to an abrupt or hard shift. At higher speeds, the shift between gears either may not be changed, or just does not feel as hard as the 1st to 2nd shift.

If this is the case, then your dealer is telling you the truth and there is nothing he can do.

Look into issues with the throttle position sensor, i had the same problem with a 95 se. The sensor is directly responsible for shift intervals as it gives the ecm throttle position which doesnt go hand and hand with rpm. Sometimes the sensor needs adjustment, however this is not recommended if you dont have a scan tool to reset your ecm. check this page out

www.vqpower.com/v2/articles.php?article_id=95