HVAC thermostat current
HVAC transformers are commonly rated 24 volts, 40 volt-amperes (VA).  So they should be capable of providing about 1.6 amperes.

40 VA ÷ 24 V = 1.666666 A

However, the amount of current flowing, depends on what load is connected. If the load is only drawing 5 mA, then only 5 mA will flow on the wire.