Check the power supply input voltage ratings. Old ones may be designed for 110v, and you power coming into you house may be above 125v. This shouldn't do much, maybe make the transformers warm to the touch, but not 70 degrees centigrade. Some older transformers are just designed to run near the core's saturation point, so, the get warm.
If you have a properly safe setup to do so, can you tell us how many ma AC the transformers are drawing on the 125v side when nothing is connected on the output.