Hi!

Then don't worry about it, if it's only getting warm, rather
than hot.

That's the thing. The outer surface of the coil does get hot after it's
been on for a while. It's too hot to stand touching it for more than a
few seconds. (It isn't so hot that you immediately pull back--there is
more than enough time to think "gee, this is somewhat hot".)

On the other hand, it has been running trouble free for some time now,
and I can't find any evidence from the original unit it was in, that the
power was in any way limited to the relay, such as by a resistor.

William