[RayDean]

A contactor is no more than a heavy duty relay.
It has a solenoid that opens and closes the contactor points.
the solenoid is an electro mechanical (magnetic) coil that when power is supplied draws the units contacts open and closed.
The contacts on the "relay" (contactor) need to be able to handle the amp draw of the ovens heater units combined.
The solenoid can be any voltage you decide, like 12 or 24 DC or 110 volt or even 220 AC.
The solenoid is independant of the relay (contactor) contacts to the heater units.

The temp controller sends the voltage to the solenoid relay that then sends (allows to pass through) the voltage through the contactor.
The controller does this by having the thermacouple in the oven judge the temperature and open and close a relay inside the temperature controller.
A thermocouple is a simple "sensor" that is heat activated in other words like the coil spring on a carburator choke.

So in a word...
Yes, you need the contactor to be able to handle the amp draw of your heating elements, if you use 2 elements you must figure the draw of both together.

Convert Watts to AMPS:
AMPS = Watts / Voltage
I = P ÷ E
Example:
2,300 WATTS = 2300w divided by 120v = 19.1 AMPS
(for 3 Phase divide by 1.73)