Just had my transmission replaced a few days ago -- now car is overheating. Related?

NO. Trainee have nothing to do with Engine over head. Make sure the radiator fluid is full. if it is not full than you have to find where is the leak

Possibility, how far was the vehicle road tested after the transmission repairs were completed?

Sometimes coolant lines, and other components that are related to cooling the engine must be removed to replace the transmission. I'm almost positive it is related.

of course it is,when u rebuild the trans, it takes the un rebuilt motor to a higher degree, u need to do it all at once or u will have problems

Maybe they punctured the radiator, or the tubing is loose. It does seem related, in a strange way.

YES IT IS RELATED, Your car is old enough to have needed it's tranny replaced, which means it is either really old, or you drive it the car to the ground. Therefore having your tranny repaired, means better shifting, BUT it means more repairs! Where is the anti freeze pouring out from? Water pump? Hoses? Engine block? WP- could be loose Hoses- might need to be replaced EB- Head gasket... Before dumping more money into the car,,,, you might want to think of ther options.

It might be your water pump gasket or the water pump its self might have a crack and also check the hoses.

your transmission being replaced should have no effect on your engine overheating, if you used a reputable mechanic. If you have antifreeze pouring out, then you need to check that spot. Also check your radiator and all your gaskets and hoses.

Yes, certainly. But only in the sense that your car is old and worn out. Things will continue to fail. Summer is here, so the cooling system is under more stress. That, or your mechanic deliberately caused damage--perhaps by jamming your thermostat.