Thermostatic Controls - Thermostat voltage DC vs AC, 12V vs 24V etc

Hello,

I have appliance (burner) which needs to be connected with thermostat. There is a choice of 12VDC or 24VDC on the contacts.

Questions:
1. What thermostats would work with this voltage?

2. Majority of thermostats are 24VAC. They are coming with different forms of complexity. It all comes down to the contact being closed or opened in simplistic terms. So does it even matter if it is DC vs AC?
Can thermostat be hooked up to 12VDC even if it is rated to operate with 24VAC? I understand that more sophisticated thermostats (programmable, energy efficient solutions) also operated by this voltage perhaps besides just closing or opening the contact...
So what would happen if such thermostat would get 12 or 24 VDC instead of rated 24VAC connected to it?
Again I suspect the simple thermostats might work as they are just switches closing and opening contacts... but... :)

Any help/advice appreciated!

Thank you.

Further thoughts / digging...

Looks like more sophisticated thermostats are just triggering relay to close contact for the appliance. I guess they (such contacts on thermostat) are just "dry contacts" (I hope this is the right term), meaning voltage suplied to contacts of the relay to be closed does not matter (well within parameters of what they are rated for of course) the thermostat just closes and opens them...

I guess I am a bit confused with voltage to power the thermostat (if it has to be powered) and the voltage on the contacts of the appliance to where thermostat is connected controlling the appliance....

Thank you.

Are you looking at using the program set back, or just set the temp and forget it?

I want to consider all oiptions given the condition to be able to choose from.

ok, Most of the honeywell basic t-stat sold at retails are a simple relay. it can be used with 12 volts.

They run on battery.