No heat. Both heater core hoses are cold. Could it be the thermostat?

We do see many heater cores get plugged in these cars. Disconnect the hoses from the heater core and GENTLY blow air through the core to dislodge some of the sediments. Flush clean water through the core to flush out any loose sediment. Installing a new thermostat is a good idea. It is also possible that the water pump is not circulating the coolant, but that would normally have other (overheating) symptoms.

Had the same problem this winter. All we did was backflush the heater core. $15 for the cleaner and about one hour to do. Videos on U-tube or take it too a shop. Easy fix.