We had your typical 25+ year-old GE double ovens that we just
replaced. The new oven uses the typical method of using a relay to
change elements to keep the temperature even.

The problem is that I hear this clicking all over the first floor of
my house. I cannot believe anyone would find this sort of clicking
acceptable. I fully understand that it's normal and that replacement
is pretty much a waste of time as the odds of getting a more quiet
relay is pretty slim.

However, I'm wondering about methods to possibly mute the sound. The
area behind the upper panel (where the relay must be given the origin
of the sound, clearly cannot be getting all that hot or else there'd
be a real problem. I was thinking about possibly adding some sort of
insulator around it or the panel to mute much of the sound.

Does anyone have any thinking on this idea? Do you think it would
work? If I did it, what would be the safest, yet possibly effective,
material to use?