its not hard to start........it changes into 3rd no worries at all.......i would have to say the thermostat isnt stuck upon because it doesnt take long for the water termerature to rise to about just below half
If you're keen, I would check to see if the ECT ECU is giving the transmission solenoids the correct signals. The ECT ECU and engine ECU sit behind the glovevox of my cressida. I have setup 3 different coloured 12V LED's in my glovebox. These are wired directly to the outgoing solenoid wires from the ECT ECU and tell me exactly what the ECT ECU is trying to do. There is a LED for each solenoid. S1 solenoid LED is red, S2 is green and the S3(torque convertor lock-up) is blue. Quite interesting to watch. I may have the wiring diagrams for your car on my PC somewhere to help identify which wire is what.
S1 on/S2 off is 1st gear
S1 and S2 both on is 2nd gear
S1 off and S2 still on is 3rd gear
Both S1 and S2 off is over-drive.
S3(TC lockup) comes on after 2nd in engaged, when the car is cruising and turns off if a gear change occurs.
It could be a tranny hydraulic or mechanical problem but I'd suss out the electrical side of things first.
Does your car have cruise control? If so, turn that off and try again.
Other than that, I've run out of ideas. Sorry I can't help any further.
Good luck.