No - sorry.
What you are doing is putting 2 loads (the coil and the light/buzzers) in series - that's not do-able because both 12 V devices now have to split that voltage and will not work.
Further, you're not even utilizing the contacts on the relays at all.
You can energize the coils with your 'temp sensors' (which are really temperature switches) and then use the appropriate relay contacts for your lights. Choose pilot duty relays because with your normally closed switches the relays' coils will be energized all the time.
Your temp switch to coils to ground cct will be fine; then you need to get 12 V to your relay contact common (center) terminals and wire your lights and buzzer to the N.C contacts. That way when your switches overheat and open, the coil drops out, and the contacts will close, energizing your lights and buzzer.
Most relays have two sets of contacts - or you'll easily be able to find some: In the sketch below you won't need diodes.
Too bad the switches (temp sensors) dont' have a N.O connection - then you wouldn't need the relay(s)
You'll also need to be able to cut the power to the whole cct to silence the alarms when not running.