I am looking for a few techniques to reduce contact chatter in a relay controlled by a 120 VAC voltage signal. The circuit uses a bimetallic thermal switch to turn a resistive heating element on and off. During transitions, the switch chatters and passes along a rather dirty control signal to the relay coil. Based on my testing, this appears to be less about setpoint hysteresis and more about the design the switch, as it doesn't have clean make/break performance. All components are rated for AC voltage at the specified levels. The relay is an Omron LY1F-AC100/110 and the bimetallic switch is one of those old-school mechanical rotary types.
In the waveforms below, you can see the fluctuating input to the relay coil, which causes the contacts to rapidly chatter. The heating element is rated for 750 W, so the contacts produce visible arcing and I am concerned about premature relay failure (as well as the rather unpleasant machine-gun-like sound).
In a low-voltage DC control circuit, there are a number of methods I could use to filter the relay coil signal to produce a clean switching action, but I am less sure about a mains-level AC application. What are some ways that I could solve this problem without overly complicating the circuit?
EDIT: Based on the comments and answers below, I thought I would share the reason for not using the bimetallic switch to directly operate the heating element. The real-world circuit has a mode selector switch between the voltage source and SW1. This switch enabled other banks of heaters and carried the entire current load. Over time, the contacts became worn down due to arcing. Using a relay reduces the current through this mode selector switch to preserve the life of the contacts.