I agree, the heat lamp (and all heat sources) needs to be on a thermostat, but as midwest said sounds like the problem would have been anyway. To me the problem is (please forgive me if I'm wrong) but the snake was able to get up too high next to the lamp. Some people don't even use stands and put the heat dome right on the mesh and don't burn they're snakes. I had mine on the mesh.
Your hides sound like they are very high up. I like the black plastic hides that are about 3 inches high which reptile basics sells when the snake is on it they don't get high enough to be that close to above heat lights. I use an infrared to moniter the top of the hide temps. You found how hot it is up where you said it was 160 degree's so you must see the need to make sure the snake can't get up close to that hot area. You might want to get lower hides. Most people have belly burns on their snakes. I would think a snake would not stay up by the heat like that and get burned but I guess it can happen. Sorry to hear it, I know you didn't mean for that to happen.
Link to the hides I am talking about easy to clean and snakes really like em.
https://www.reptilebasics.com/hide-boxes
I see now the cage isn't very high up. Uhmm