I put in a replacement thermostat, Honeywell RLV310, and the surface gets very hot. Any ideas, or it this OK?

Don`t think I would use it till I found out why,, I would double check the installation,, make sure all the connections are tight,,

If it has the backlight on all the time, it will get warm. It's best to leave it off.

That is a line voltage thermostat. Make sure all wiring connections are tight.

Honeywell RLV310 Digital Manual Baseboard Heat Thermostat

If it's a line voltage stat, then loose connections will definitely do it. If the connections are clean and not discolored or can be cleaned up and tightened, you should be OK too.

If the internal contacts are pitted, then the stat should be replaced. You won't be able to tell this, but a voltmeter used properly could.

It is a replacement stat so the contacts should be OK but you never know.

I have baseboard heat throughout the house and have 6 of the RLV310's installed and the side of the thermostat gets warm, but not hot when the thermostat has the heat on. If you take the cover off the thermostat, you'll see a giant heat sink that occupies almost the entire portion of the unit to the left side of the LED screen. I think that the heat you're experiencing is just a result of the thermostat's heat sink doing its job, but if you are concerned, you should call a licensed electrician to check it out.

That is a TRIAC switched thermostat. They will get warm, but they shouldn't get HOT unless something is wrong. The heat sink is why they are so big. I don't really like them. To me, mechanical switches are much more reliable.