2002 VW Jetta 1.8T: Coolant temp began rising to

1st check fuse to the heater
2nd check relay
3rd the filament wire of the heater

You have a air pocket in your cooling system!

Have you verified that system has been "burped" of air? That the fans kick on? Check radiator hoses for kinks. You can try running without the thermostat to see if that helps and can identify if the thermostat could be a problem. You may need to check your coolant mixture too.
Sounds like you have reduced flow or restriction in cooling (heat exchanger) as it runs fine at cooler temp but can't keep up when it gets warm.
New parts don't always equal working fine parts.

I WOULD CHECK BOTH RADIATOR HOSES TO MAKE SURE THEY ARE HOT. THERMOSTAT COULD BE STICKING SLIGHTLY CLOSED.CHECK COOLANT LEVEL MAKE SURE COOLANT NOT LOW.IF COOLING NOT BOILING OUT OF THE EXPANSION TANK. I WOULD HAVE CAR HOOKED UP TO A DIAGNOTIC SCANNER AND CHECK COOLANT TEMPERATURE SEE IF TEMP. OVER 230 DEGREES IF SO RADIATOR COOLING FANS NOT WORKING.COOLANT THERMO SWITCH BAD BOTH FANS SHOULD BE RUNNING AT LOW SPEED.IF ALL LOOKS GOOD YOU COULD HAVE FAULTY LOW COOLANT SENSOR IN EXPANSION TANK.MAKE SURE COOLANT IS IN THE EXPANSION TANK BECAUSE COOLANT LEVEL COULD BE LOW.ADD COOLANT IN THE EXPANSION TANK UNTIL YOU AT MAX LEVEL LINE ON THE EXPANSION TANK.DONT OVER FILL THE EXPANSION KEEP ADDING COOLANT UNTIL COOLANT LEVEL STAYS AT THE MAX LEVEL LINE ON THE EXPANSION TANK.

Have you checked the coolant level in the overflow tank? Make sure it's to the proper level. The coolant warning system can lose its little brain on the VW's. Sorry I can't be more helpful.

Check your coolant level and condition. If you havent' replaced the coolant in a while then change it. You can drain it from the bottom of the radiator plug. You may also want to change your oil and oil fiter.

1) Is there enough coolant in the radiator?
2) Have you noticed if the electric fans are kicking on when the temp is going high? I'm guessing that they are not, the temp switch may be faulty.

sounds like you got stuck pretty good,.....could have knocked a wire off the cooling fan, or punctured something to make a leak of the coolant,...check coolant level, let it run and see if fan comes on as the temp is increasing,.....good luck, cracklin joe

From what you have posted, it sounds like your coolant level is low. With engine cold, re-fill the system, then check carefully for leaks. One leak has been located you can take necessary steps to correct it.
Generally the reason for your problem symptoms is that the coolant level has dropped below the level of the cylinder head. This can cause the head to overheat and warp, bloww a head gasket, or both! (both substantial $ to repair) DO NOT drive vehicle with this condition, till you have found and corrected the problem!!!
Good Luck!!

coolant level is fine still no heat