old thermostat issues (maybe?)

So I found a document that says my magnum stoker was purchased in 1993. The thermostat looks like it is probably that old as well.

It still works, but it seems like it's maybe sluggish (the thermostat). Cause my wife just opened a door to the outside and let a cold draft in, and the thermostat is just taking forever to go down below what should kick on to constant feed state rather than maintenance state.

Is it fairly easy to replace the thermostat with a digital one myself? Or is it possible that's not even what is going on here.

Starting to wonder if I even need the thermostat. I have it set up for a medium burn (2 dot travel on the pusher) and its been keeping the place toasty, but not too toasty.