Is cost/availability of the thermostat the issue? If the part # is 132-44, the first couple hits on Google.
Perhaps there is yet another "modern part" as Aussteve says that is less expensive.
I'd think a "solid-state" timing circuit that performs the same function could be assembled for, say, $5 in parts but would involve working with small electronic components, soldering, etc. If that's your interest I'd re-phrase the question as such in the Electrical Forum.
