In the video posted below, I was controlling the heater by simply cutting the power supply to it. This was good because it meant that I hadn't played around with the built in safety features, but bad because it beeped every time the power cycled. Time to break out the screwdrivers!
The built in controller
The built in controller is fairly simple and I quickly figured out which was the signal between the two boards that caused the relay to switch. I then had a think about if it was safe to drive that relay myself, or should I be putting a second on in series with it, meaning I've got a fail safe with the on board temperature controller if my controller forgot to switch it off. I can wind the on board one up to a temperature at the highest level that I'll ever want, and that is as hot as the room will get in the event of a failure.
40A Solid State relay
I discovered when I went to my local electronics shop that they had some rather grunty solid state relays available for around $45 each. I grabbed a handful of 40A AC ones and one 100A DC for another project.
It fits in the space!! :)
As I said, I wired it in series with the existing controller for safety reasons. I'm not much of a C programmer so I figured this was the best option.