24VAC 50VA Transformer Gets Hot With No Load—Is This Normal or Harmful?

If I have a simple 24vac 50VA heating system transformer hooked up to 120vac and do not have a load connected to it it seems to get hot after about 5 hours. Is there a problem leaving it powered? Will it eventually burn up without a load on it?
If so can I put a resistor across the secondary to maintain a minimum load and keep it from overheating and what size resistor should I use?

Along the same lines - if we power up recessed fixtures with magnetic transformers in them and no lamps connected is that harmful to the transformer? Probably your next question and if there is only one connected, what if there are two, three, etc. They do have thermocouples wired in for overheating but I don't think that will add any load to the transformer.
Thanks in advance for advancing my knowledge on simple circuits.

It is highly unlikely that the transformer heating will be reduced by adding a minimal load. Assuming there is nothing wrong with the transformer, the heating is most likely caused by core loss. If this is so, then there will not be any way to reduce the heating of the transformer.

You can do a quick experiment to verify this by putting a 5W 250ohm resistor across the secondary and measure the change in temp. This should draw around 2.5W from the transformer (the resistor will get hot, a fan might be a good idea) and my guess is that you will not be able to measure any change in transformer temperature from the zero load case (make sure the transformer is not being cooled by the fan if you are using one).

Assuming the transformer is well designed, getting warm should not be an issue.

It is not harmful to run a standard AC transformer with no load.

You might want to look into switching power supply replacements for the transformers. They can be significantly more efficient, both with no load and under full load and therefore can generate significantly less heat.

You want to be careful about running the transformer based lighting on a dimmer (follow manufacturer's recommendations) and if you do change over to a switching power supply be aware that some are rated for being on a dimmer and many are not.