I'm with Steve, although I'm ambivalent about which controller philosophy you choose since you seemed to be willing to just "dial in" your desired temp so any thermostatic approach will be a big simplification to that.
The reason you want to go with "on-off" switching instead of a potentiometer is the pot is wasting a fair amount of power in this low-impedance 240V circuit. Not only is that a hit to your power bill but the cost of the components at your high power levels is pretty pricey. (I'll note that, if you're using a kitchen burner, that it was also using an "on-off" approach in its control knob.)
Now instead of a pot, there are electronic approaches (SCR-based phase angle control or pulse width modulation, etc) to a single-knob constant-power delivery, but those parts are also more expensive than a simple on-off relay and controller for it. And although on-off temp control will give you slight temperature ripples, constant power delivery to an element does not mean constant cook temperature. The temperature and wind conditions outside and the increasing temperature of the meat inside all serve to make your cooking temperature somewhat independent of cooking power.
On-off controllers account for that by using an internal thermometer which is the input to the controller to determine when to switch power to the element and when to switch if off. This is particularly important for long cooks like smoking meat.
