"You" wrote

Should the alternator run that hot?

that's why they put pullys with fans built-in on alternators,
to blow some cool air thru the alternator windings.......

Would low speed caused by slipping belt cause overheating?

Not having enough air blowing thru the alternator, due to
slow speeds will certainly cause the alternator to get Hot.....

Possibly - Perhaps the heat output of the alternator and the cooling
produced by the fan are not matched. But, would running at a higher speed in
fact result in a cooler alternator?

Heat produced is proportional to square of current, so heat produced should
increase dramatically as speed increases. As the current (speed) increases,
then cooling capacity also needs to increase.

It would be interesting to see if typical alternator fan air flow increases
in proportion to the heat produced. I somehow doubt it - they are more
likely sized for the maximum and should therefore provide more than enough
cooling at idle speeds.

Thanks for all the input - I won't worry about my hot alternator and I do
carry the old 35A unit as a spare along with several belts!

GBM