During a heat wave, it's not always the temperature itself that's a problem. It's that the heat is unremitting––you don't get a break from it. It's sweltering hot day after day after day.
You'd think the word unremitting would be connected to the word remit, but that's true in only a loose way. Remit means to send back––but if you remit a debt, you forgive it, or lift it. Unremitting describes something that is never lifted or sent back. Like the Energizer Bunny, it keeps coming and coming and coming.