Controlling AC819 RF433MHz transceiver for boiler control


I’m trying to to control AC819 transceiver which is wired to my boiler (picture attached).
It is controlled by AC205 wireless thermostat (433MHZ).

Trying to decode with Audacity (see attached), but doesn’t seem to be any clear pattern.
(I have a suspicion that it’s not really 433Mhz, because I don’t see any strong signal
on the Audacity trace)

Can anyone explain how I could wire this relay to an Arduino … i.e. use the Arduino
to switch boiler on/off? Preferably in parallel, so that I could still use the wireless
thermostat … and the Arduino to turn boiler on/off

Best regards