Does not up shift to third or forth gear soon as it should.

it needs transmission work, worn gears

It always starts out in first, it's a 3 speed automatic, that's what automatics do. they start out in first and at about 15-20 miles per hour , they shift to second gear, and when the speed is about 35-45 MPH, the transmission automatically shifts into third gear, or Drive.

Bigger automatics have 4 or more speeds. Till recently, 4 speeds were the norm, and fourth gear was often dubbed Overdrive, as it allowed the engine to run slower in 4th gear, than it had to maintain speed in 3rd gear, drive. It's good, it increases your mileage per gallon of gas, so you save that way, but like all things more complicated, they cost more to fix when something goes wrong.

Check your range sensor!

my van is doing the same exact thing but the othe day it was perfectly fine no slipping i went about 25 miles and i started off from a stop the engine rev and tranny slipped and the van died i restarted the van it runs great but acts as if there is no transmisson does not take power frm ngine when shfted does nothing please help

Sounds like the band that controls 3rd and forth gear is almost worn out. Have you followed the recomended interval for transmission fluid changes? What does your trans fluid look like?

Let me see know at 45 miles per hour a vehicle usually shifts gears into the highest gear so could it be the torque converter hanging up and not shifting quick enough or maybe its the U joints. Have the transmission fluid checked for proper level and color.
Here's a small test for you when your accelerating up to 55 miles per hour try letting off the pedal at 44 miles per hour and then reaccelerating up to the 55 mph and tell me if it`s smoother if it is then chances are that it`s hang up on third gear. There's also a electric sensor located on transmission that assist shifting it`s usually controlled by the engine timing.
One more thing did the repair man check to see if the tires where directional tires if there not put on right it could cause vibration and early wear out .Hope i helped you.

brake band worn out ?? hence the smoke where its slipping and getting hot

The throttle position switch has some effect on shifting but should effect both hot and cold. It is normal for Toyota vehicles to lock out the overdrive upshift (3rd to 4th gears) until coolant temperature reaches approx 180 degrees f.

once hot it presents this problem?..when fluid pressure is lowest is when it is hottest...can you service transmission with new filter and fluid and be sure all lines up to trans cooler at bottom of radiator are clear?