Esp8266 + Relay, yet another post..

With the relay energized for 5 minutes or so, measure the voltage from emitter to collector, should be only a few mV (< 100), feel the transistor with the tip of your pinky finger (carefully) it may be warm but shouldn't be "spit sizzlin" hot, (< 120 F) or so.
Most TStats here in the US work on 24VAC, don't know about EU and ROW.