I guess it depends on what you mean by "hot".

The general rule of thumb is, if you can hold your thumb on it for 30
seconds, it's not too hot.

Most coils these days are wound with wire insulation that can stand at
least 85C if not 105C. Your thumb isnt going to like more than 60C for
a few seconds.

You also have to consider what might happen if you under-drive the
solenoid. It might fail to pull in, then you have a problem. Also
some solenoids used on AC will actually get HOTTER if the plunger
doesnt pull in. The lack of iron will reduce the coil inductance,
which is not a good thing.