said by Gemstone:The control transformer is part of the oil burner (Riello)... It is marked as 24VAC output... Only has 2 terminals... I measure 32VAC across the terminals...
I think it's what alphapointe
said; it's unloaded, your meter may be off. Peak voltage on 24VAC (RMS) is 34 volts.
FWIW, I did what you are doing. I replaced the round one with a new HW stat similar to what you are doing. In my case it operates a relay but the voltages are the same.