PWM a heatgun using a relay
Your home electrical system will not be damaged by this, but you might get interference on a TV or radio as the relay switches. As suggested, you don't need to PWM very frequently -- every few seconds should be OK.

What are you trying to regulate ? What regulates the PWM on-time ?

Instead of a relay, you could use a triac (like in a light dimmer), although finding a 2 kW one might be difficult. A triad only switches off at the zero crossings of the AC signal, and will therefore generate less interference than a relay.