To answer your question: Likely huge, also likely not a good idea without circuit changes.
Take a look at
https://www.electronics-tutorials.ws/rc/rc_1.html
or similar. Google capacitor charging or similar.
But, other questions are probably better asked first.
Why?
Often heaters have significant thermal inertia, meaning that they heat up slowly and cool down slowly. This means that their temperature tends to be a smoothed version of the power going in anyway. Is there a strong motivation to smooth the input?
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If the PWM ran faster, it would give the heater less time to heat & cool beteween changes, be smoother in that the heating and cooling times would be shorter, so the heater instantaneous temperature would vary less.
If you put a capacitor directly on the output of a PWN, then the PWM circuit is seeing a quite different load: it may need changes if it is not to expire.
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So, a few more details?
What sort of heater, PWM supply, powers?