Contact arcing, how to avoid?
My first point is that you might find that the mechanical thermostat is cheaper than the capacitor to achieve the same reliability. My 2nd point is that adding an extra component is potentially halving the MTTF (mean time to fail) of the system. It could be worse than that - the capacitor could, in certain circumstances make the problem worse (3rd point).

With a resistive load (the heating element), there will be an initial surge of current as the contact closes because the resistive element is cold. If you put a snubber capacitor across the contact then this snubber will have been charged from the previous opening of the contact and now, when the contact re-closes, it will see the normal peak associated with the element plus a discharge from the capacitor. In other words you' might make the thing fail quicker than before.

It's unlikely that there is much inductance in the element so the contact opening isn't going to create much of a spark so I'd say the bigger issue is when the contact closes and a snubber capacitor won't help.

Advise - try and understand the mode of failure then conjure up a decent fix