In article le.rogers.com,
"larry" writes:

Way back, when I was 7 or 8 years old, (I am 55 now), my dad got me an
electric train set....During that Christmas we were at my Grandparents place
and they were on 25 hz power....At home we were on 60 hz power...

We had to be at home for me to try out my new train set.

What has that got to do with this question?...

This....

I have a number of transformers and would like to experiement using then at
a higher frequency....let say 500 hz and / or higher.....

Would they still work?...I am assuming so...

Should not be a problem. Designed for 25 Hz operation, they have
a lot more iron in the core than those for 50/60 Hz. That means
they are HEAVY. [it's a mechanical mounting problem only]

Would they run cooler?....

Not any more than audio amplifier power output transformers at
the same wattage.

Could anyone foresee any negative effects?....

Other than physical mounting places having to be much more
sturdy, no problems at all.

Aerospace electronics went to 400 Hz (and higher "wild" supply
frequencies) some time ago to save WEIGHT. For the same
power handling capability, the core size could be smaller for a
given core flux desnity in comparison to 60 Hz.

You WILL get heating and inordinate core losses and loss of
efficiency of power transfer in trying to use a 400 Hz transformer
at 60 Hz.

You will NOT have any of those problems on getting a lower-
frequency transformer to work at a higher frequency.

For common transformer iron laminations, the upper end of
frequency response...where all the effects others were talking about,
would be above, perhaps, 5 KHz to 10 KHz. Those other effects
would only begin to show up at that limit frequency, getting worse
at higher frequencies.

In the old vacuum tube "Hi-Fi" music amplifers, output transformers
needed a BIG core cross section to reach down to 30 Hz. The
upper end of response was determined primarily by the distributed
capacitance of the winding with the most turns, secondarily by the
iron alloy of the core. Mutual inductance effects didn't much come
into play - regardless of what some instructors talked about in
classes to illustrate "points" about mutual inductance. :-)

Len Anderson
retired (from regular hours) electronic engineer person