I have electric baseboard heaters as well. Today , they kept pumping out the heat. I changed the batteries and turned the heat down as low as I can but it still didn't work. Any suggestions?

If you have a line voltage thermostat, I would say the contacts inside the thermostat are stuck closed. If it's a low voltage thermostat, It will be controlling a relay and it is stuck closed. Not knowing what you have its hard to say. I hope what little info I gave helps.