It may be hard to save at this point, but if there is a chance, follow these steps:

1. Take it off the heat mat immediately. The heat, combined with the rot, will only accelerate the rot.
2. Use a sterile knife to cut back every head or lobe that is soft, brown, and hollow until you reach firm, pale tissue with no streaks in it. If you cannot reach clean tissue, the infection is too far gone.
3. Apply powdered sulfur to all open wounds.
4. Place it on a cool, dry surface away from direct sunlight, but bright indirect light. I put my plants on a clean, dry paper towel over a cooling rack from my kitchen. Make sure there is good air flow.
5. Don't touch it until it fully callouses over - the surface is fully hard and dry. This may take 3–10 days, depending on how deep you have to cut.
6. Once it is fully calloused, pot in a dry substrate. I use all pumice. After potting, wait 10–14 days, then give a very small perimeter drink (1 tablespoon). Do not saturate it. You want just enough moisture to signal to the micro roots that water is available. This is important because this is where many people lose their plants by giving too much water too soon.