Is this my doorbell transformer?
Anything is possible, but my bet is on a thermostat transformer. Typical (US) thermostats run on 24V AC. Typical doorbells (though there seems to be less consistency than with thermostats) use 16V AC.

Get a multimeter. Test the voltage:


24V - Thermostat
16V - Doorbell


Something else? Post it here and we can try and figure it out.