> I'm looking for something that has a 1 degree (F not C) hysteresis...

Maybe not what you're looking for, but if you're just looking for a 1F degree lag in temperature change, you can also try just increasing the heat stored in your house's thermal mass. For example you could add something with high thermal mass (i.e. concrete) to the place you want higher thermal lag, and position it so it soaks up a lot of solar radiation. That'll buffer out your temperatures.