Controlling hotplate by power source
You may find that they use what is called an "infinite heat control", which is an electromechanical time-proportioning controller that works similarly to a light dimmer. It works by switching the power on and off with a varying duty cycle that is achieved mechanically (with a bimetal strip and mechanical contacts). 

On the other hand, there may be some kind of crude electronic controller in there like a light dimmer. Perhaps with a triac and diac phase control. 

In either case, chances are it will be unsuitable for use directly because of a lack of galvanic isolation. You may be able to repurpose the triac (if there is one) by adding an optotriac isolator to it,  but an SSR would likely be easier and safer. 

In any case, you do not likely want to control current, you want to control power directly if possible. The best way to do that is to chop the power to the element so that the power is linear and proportional to the duty cycle. 

P.S. If the knob moves easily like a light dimmer, it's probably an electronic control. If it's a bit harder to turn, like a home range top adjustment, then it's probably an infinite heat control. 

In any case, grab a screwdriver, pop the cover and have a look. All should be clear.