I have a dedicated 20 amp circuit for a 240V, 1000 watt, 4.1 amp baseboard heater in a small bedroom. I would like to replace the current thermostat with a programmable thermostat. The only programmable thermostats I can seem to find are rated for 15 amps, not 20. Since the heater only draws 4.1 amps can I use the thermostat rated for 15 amps on the 20 amp circuit? Thanks for the help.

You should be able to do that. As long as all the wiring is rated for 20 amps you are fine. It's just that the tstat will not handle that load. Just keep your loads within it's rating and you're fine.