Agree with Zombie that the Specs refer to input voltage. However, I’m not seeing any way to make it work without external circuitry.
When it’s in a “heating” state, it’s essentially closing an internal relay which makes a connection between common and normally-open. When the relay is not energized, it’s making a connection between common and normally-closed. Just like a light switch completing a circuit.
You’re trying to turn on two separate circuits with the same internal relay which are different voltages. I don’t see how a suicide cord (cord with male fittings on both ends) fixes that problem. However, I’m probably missing something. Zombie, I love learning new things, so a “back of the envelope” circuit diagram would go a long way.
Otherwise, the only way I can see this working is to build a circuit that uses the Ranco’s internal relays to energize two external relays: one for 120VAC and one for 24VAC. A switch to turn on a switch.