I see...
No, wait-I'm confused. DUMBFOUNDED as it were...
The simplest power controller is an infinite gain (on-off) type that
turns the power full on if the temperature is low and turns it off it
the temperature is too high. A comparator is a device that switches
off or on depending on which of two signals is more positive.
Based on the power of the heater, the heat stored in the heater
element (that keeps coming out for a while after the power is turned
off, and takes a while to come out when the heat is turned on),the
thermal mass of the object being kept hot, and the time delay between
that mass and the temperature sensor, the temperature will ramp back
and forth through the desired temperature. Whether or not it stays
within the required bounds under this method of control depends on the
the factors I mentioned earlier.
The only way to keep the temperature in much narrower bounds is to
pulse the heat faster than the time delay between the heater and the
temperature pickup, and vary the duty cycle of those pulses with a
more complicated scheme than the simple one I first described. One
such more complicated scheme is the PID algorithm (a combination of
Proportional gain times the temperature error, another gain times the
integral of the error, and a third gain times the derivative of the
error.