Hello. I am replacing my manual heating thermostat with a digital thermostat. There are two identical black wires coming from the new digital thermostat. How do I know which one attaches to the live (red) wire coming out of the box? Will I damage the new thermostat if I hook them up wrong?

What kind of heater is it? Electric baseboard/ gas furnace/ etc. If electrical, how big & what voltage?

Read the instructions. I've learned a lot that way.

If there are 2 identical wires it may not matter how they are hooked up... I would encourage you to read the instructions. If this is to control 220 volt electric baseboard the 2 identical wires may be a pass through for one of the legs. Again I encourage you to follow the instructions