I'm working on an ESP8266 thermostat that should be powered by the 24V AC from the furnace. I'm looking for a converter to 5V DC that would be small enough to fit in a smaller enclosure and not dissipate too much heat. Not fully sure about the current, but I'm planning for up to 500 mA for short periods of time. I found on ebay this, but it accepts input from 85V upwards. What would happen if I would feed 24V AC to it? Would it still work. Or alternatively doesn anyone have a link for something similar that would work with 24V?
Transformers for furnaces are typically Class 2 transformers, energy limited. Unloaded, or lightly loaded, they produce a significantly higher output voltage than the rated output voltage, 24 volts in this case. 28 volts is typical, and it may be higher during high line situation. The 24 volt rating is a loaded voltage, with a resistive load.
28rms x 1.4 = 39.2 volts
You should be using a regulator with a voltage rating of at least 40 volts, and that is really marginal.
The AC-DC converter you linked to would not work. It has a low voltage cutout. It also would not be able to provide the power if it was able to work at the lower voltage. The input current would be much higher than the normal input current at a normal line voltage.
24VAC rectified with a full diode bridge rectifier (4 diodes) becomes 36VDC when smoothed with a cap, the datasheet indicates this part would be okay with that. You'd probably be okay as you're planning <500mA output most of the time.