While a vacation on December-January the termostat was on 55F, after returning home set up termostat on 72F but it is not working. There were few really cold days on January. Could it be something broken? How to fix it.

Hi Valentyna and welcome, you need to give more info to get a good answer, brand of heater, electric or gas, plus any sounds the heater make. Good luck

If your thermostat has batteries , they could be dead. Pull the cover off and you will see the batteries , if it has any.Replace them and put cover back on .

The transformer could also be bad. In order to know for sure you will need to use a meter to find out what is wrong.