Got to patch dem leaks!
Step 1: Find the holes
Once you've marked all the leaks (mine had two), set it out in the sun to dry.
Step 2: Plug the Holes
I opened the valve to deflate the Thermarest before applying the epoxy so that the air wouldn't blow a path through the curing epoxy.
Mix it up on a piece of cardboard pulled from the recycling bin and dab it over the place you marked with the sharpie.
Let it set for a few hours and then test out how well it holds air!