Yeah, automatic transmissions are very sensative to heat. Heat will actually kill an auto trans as quick or quicker then just about anything else. Not sure if the overheating actually caused the no reverse problem, but I am sure it didn't help.
Is it the three speed trans, if so, probably the TH350, and about $800 - $1,000 to rebuild at a trans shop, depending on your location.
I agree to start with a flush and filter change and see what happens. Worst case is you spend $30 and it doesn't work
Sure, it is $30 and might help at all, but it might also fix the problem and help avoid costly repairs.
Was there any signs of reverse going out before this? Was it slow to shift into any gear, or slow to go into reverse when cold or hot?