I tried to turn on the heat, the thermostat will let a/c run but not the heat.. could this be a bad thermostat?

Yes it could be... and a lot of other things too.

Can you provide more info: is this a new installation? Has it ever worked? What kind of thermostat and furnace are they? How many wires are in the thermostat. Where are they connected. Is the thermostat turned on to 'heat'. What troubleshooting have you done so far?

Go to the sequence of operations in the sticky at https://www.askmehelpdesk.com/heating-air-conditioning/heating-cooling-maintenance-repair-troubleshooting-frequently-asked-questions-58313.html

Observe what happens at the furnace when the thermostat calls for heat. Some furnaces have an LED that blinks a code. The codes are often on the furnace door.