I doubt that anyone is really using a true "rheostat" to control the power to their smoker heating element.
People sometimes use the word "rheostat" (incorrectly) to mean a power controller of any type.
Technically, a rheostat is simply a variable resistor. This is distinct from a potentiometer in that it has only two terminals versus the three of a potentiometer.
For a rheostat to be used to control the power of one of these 800 to 1200 Watt heaters, the rheostat must be sized to handle dissipating the power created in the portion of its resistive element that has been set to be in series with the heater. The worst case ends up being near one end of that element when you've adjusted it to give almost, but not quite, full power to the heater. In that range, the current through that small section of the element will be near its highest, and that heating will be concentrated into a small area of the element.
Thus, usually, rheostats will be rated for a maximum current rather than a maximum power dissipation.
In any case, a true rheostat would be very large to handle the current that one of these smokers' heating elements would draw.
Further, using a rheostat to control the power to a heating element becomes rather unintuitive because of the non-linear relationship between the amount of rotation of the knob, and the power to the load. Sometimes you see specially-wound rheostats that have a non-linear character designed to compliment a specific heating element or load so that the power to the load will be somewhat linear with respect to the rotation of the shaft.
But what people normally mean, when they say "rheostat" is an SCR or TRIAC based phase control device like a lamp dimmer.
Most SCR-based units use "back to back" SCRs to achieve full-wave control. These are usually more rugged than the TRIAC-based units.
Nobody really uses rheostats these days. And even in the past, for high power applications, people usually used variacs (variable transformers) to both maintain linearity of control and efficiency.
So I'm pretty sure, when someone says they are using a rheostat to control their smoker, what they mean is that they're using a phase control device.
You can get small phase control units meant to control the speed of small motors and the like. And that's likely what folks mean by "rheostat" these days.
I, too, prefer an actual temperature controller. And I prefer a controller that employs proportional control so that temperature cycling is minimized. PID is nice, and very inexpensive to implement these days, so that's what you often see.
In any case, as tallbm and others have pointed out: It's almost a blessing that your unit's controller has failed. A better controller may well be a noticeable improvement over the stock system.
But be advised: You will need a different means of generating the smoke if you go with one of these replacement controls because the heating element won't cycle on full blast at times the way the stock controller makes it do. So the chip burner won't work.
