It would certainly help if you posted any type of hint of what vehicle you are asking about. If you don't want to list it in with your question then maybe take a minute and list it in your profile or signature.
On Ford diesel trucks there is a coolant hose that goes to a tranny cooler, but I doubt a dead battery would effect it.
Wonder if a low battery might interfere with the signal of the transmission cooling solenoid operation?
A defective solenoid can cause the transmission to run hot.
The transmission solenoid regulates how much fluid is passed through the transmission. If it malfunctions, not enough fluid is pumped into the transmission, which will result in the transmission overheating. A defective solenoid has to be replaced. A thorough Vehicle Courtesy Check of your transmission overheating issues should be able to identify the solenoid as the problem, but sometimes the underlying circuitry can be the issue. Either way, the solenoid should be checked if all other issues have been addressed and your transmission still overheats.
Also, the question, how are you determining the transmission is "over heating"? When I recently had a "dead" battery, it triggered all sorts of warning lights. None of the warnings were valid, and cleared once the voltage, battery replaced, increased to a normal range.