Hello: More chipping… There is no thermostat I know of that can be used to control a standard gas heater, without replacing the existing control. I’ve looked for such a beast, with no luck. With the cold blast idea, I’m really talking about two different systems (although they both use the water heater as the heat source). One is the space heating system. which I imagined has a loop of water that cools down to ambient when it isn’t running. The other was domestic hot water. If the heating pump were to shut off for a bit daily (instead of running continuously), on starting back up it cound provide that cold blast needed to kick the thermostat on.
I understand your reluctance to use a boiler. My place needs 27,000 btu at design load. I have a gravity driven radiant system, with a 40 gallon, 35,000 btu heater as backup. Wood is my backup of choice though. A boiler would likely be far more expensive and complex, aside from being about impossible to size for this load.
Not knowing the details of your system, understand I’m making some wild guesses about how it’s put together. Whatever, there likely is a way to make it perform as you would like… Variable speed pumps are being introduced to the US market, and that may be another option to allow a greater delta T in the heating loop.