Toyota Repair: Toyota Camry-1995 - overdrive, toyota camry 1995, engine tachometer

Question
Hi Ted,
I have a 1995 Toyota 4 cylinder camry with the automatic transmission, has 148000 miles and is in great shape. Last year Sept while driving its timing belt broke (previous owner told me that he has replaced the timing belt on time), I took it to local mechanic and he replaced the timing belt and water pump, but after that we noticed one problem (not sure earlier this problem was there) but as winter started (I am in Minneapolis and this year its quiet cold), when I start the vehicle transmission shift till last gear but wont shift to the overdrive and if it shifts then it works like charm and no problem, I took it to the same mechanic and he replaced the Trans oil and solenoid valve but no difference, I did some research and came to know, keep the engine idle in N and I tried that and it worked, now my observation is, when I start the vehicle after some time (don't know exactly but say after 2-3 hour), means early morning or when I return from work, after start all gear shift perfectly fine till O/D, and engine tachometer shows RPM 3000 at speed of 45-50 means O/D has not shift, then I have pull the vehicle on shoulder, idle it in N for 1-2 minute, so engine temp indicator goes up a little bit and after that when I drive, O/D shift like normal and continue normally even I stop and start the vehicle at signal or after 40-50 min, one more exception, if speed goes above 35-40 and O/D has not shift then it will not shift afterwards, means it will shift when speed is 35-40, otherwise not, then same procedure take to shoulder, I've been told by mechanic that there could be a problem with transmission, but my argument is then how come it works normally once it is shifted, if O/D has problem then it has to give every time not the first time after long halt, I also did some research, and came across there could be problem with engine Temp thermostat or with the speed sensor, but I am not able to locate it, if so is this something I can repair or does it require a new transmission.  THANK YOU

Answer
It sounds like the engine may not be getting to operating temperature fast enough which will not allow overdrive to engage, I just had the same condition with a corolla about two weeks ago, it took about 20 minutes of driving until the temp gauge went up to the middle, replacing the thermostat caused the engine to come up to operating temperature faster, within about 3 minutes, solved the problem so I would recommend replacing the thermostat first, the thermostat is located inside the housing where the lower radiator hose enters the water pump inlet, a speed sensor or solenoid problem would turn the check engine light or the O/D light on.