Trans Won't Engage

I was wondering is anyone had a similar problem.
I have a 1989 Firebird with the OD Automatic transmission.
Every so often, when I'm driving, the transmission won't go into third or OD.
It happens when the transmission is up to operating temperature, and it happens when the trans downshifts to pass.
It shifts down to 2nd, then won't slide into 3rd when I get up to speed.

It's not so bad on city streets, but it's happened a couple of times on the freeway, and runs dangerously high on the tach.
I have to slow, and get off the freeway, as it won't engage 3rd or the OD.

Problem goes away when the transmission cools off again.
Nothing is overheating, it just happens every so often.
But I don't want to overrev the engine.

Is there a sensor, or something that may cause it?
It shifts fine when it's not quite hot.

C.

trans may be shot. but you can still try the basic routine. readjust the tv cable, change fluid and filter with a bottle of lucas transmission fix.

Sounds like the throttle valve (TV) is sticking. Do as suggested above and change the fluid and filter..but change ALL of the fluid. Take the going from the trans to the radiator (should be the top line on the radiator). Hook a good length of hose to it and put it in a bucket. Have a funnel in the trans dipstick tube and a couple gallons of trans fluid open and rrady. have someone start the car and watch the hose in the bucket. Old nasty fluid should start coming out. Add fluid to the trans and keep doing so until the fluid coming out of the hose is nice and clean. Shut the car off, hook the line back to the trans. Drop the pan and change the filter. Put pan back up with new gasket and refill the trans.
Drive it around and see if it still does it. If it does there is another thing we can try.

Sounds like the throttle valve (TV) is sticking. Do as suggested above and change the fluid and filter..but change ALL of the fluid. Take the going from the trans to the radiator (should be the top line on the radiator). Hook a good length of hose to it and put it in a bucket. Have a funnel in the trans dipstick tube and a couple gallons of trans fluid open and rrady. have someone start the car and watch the hose in the bucket. Old nasty fluid should start coming out. Add fluid to the trans and keep doing so until the fluid coming out of the hose is nice and clean. Shut the car off, hook the line back to the trans. Drop the pan and change the filter. Put pan back up with new gasket and refill the trans.
Drive it around and see if it still does it. If it does there is another thing we can try.

As I'm transferring fluid..is it better to leave in park..Neutral, or put the parking brake on and shift thru all the gears?

Also, I think there's a shifter cable problem anyway, as I can't physically shift the handle down to low.
Trans works in low, just the shifter won't move down.

C.