There should be a way to add and wire in another simple single function aquastat or temp controller. In series. With an external probe. Stick it's probe somewhere it can see you water temp. When temp drops, it cuts power. When it sees the temp back up, it switches power back on again. If I am reading you right.
There is likely a double acting aquastat out there somewhere you could replace your existing one with that might do the same thing but not sure what one. Maybe an 8124? Don't know anything about Hardy though or what you have now.
Or you could find a flue temp stat. I have one on my boiler, that controls the boiler circ. Starts it when it sees flue heat, stops it when the flue heat drops to set point. It's wired parallel with I think an 4006 aquastat (has an A side and a B side). So either can start/stop my circ - the aquastat takes over if the boiler gets too hot. Mine came with my boiler, not sure where to find one after market. Circs & fans act different in those situations - if things are hot you might want to be starting a circ at the same time you'd be wanting to stop a fan. But something should be out there to make it happen.
A good heating supply place should be able to figure something out for you. Or a good OWB dealer if you can find a capable one.