Question: how many amps can thermostat wire handle?
Answer: The thermostat wire is sized for mechanical durability, not for current carrying capacity. Codes may require the circuit to be Class 2, 30 volts and 100 VA maximum, usually 24 volts and no more than 4 amps. It could be much less than 4 amps and most of the capacity may be required for the relays in the HVAC unit.