Controlling a 3 wire AC 120v heater with relay

You may already be aware but still, use a solid-state relay (SSR) rated for 110VAC (load), 5VDC (control). The current rating can be calculated using the heater's wattage. If its 1kW then current will be 1000/110 which is approx. 10A. So choose a SSR rated for atleast 20A.

Note: SSRs are not very suitable for fast on/off. If you want power control then its better to use thyristors. SSRs can be used for simple on/off that mimics human usage.