Having an UTH is fine just make sure there is something on it. I normally tape a layer or 2 of papertowel down on top of the glass and under the substrate. This will help reduce chances of thermal burns if you do not have a thermostat for the UTH.

The "terrariums" made for reptiles have a sliding top that you put a peg/plastic pin in to prevent from sliding open. These are the best to use for snakes if you are using a tank.

The most you can do for now that I could think of is to put something heavy enough(like a book or brick) on top of the screen. Heavy enough where the snake will not be able to budge it at all. Check for gaps. If there still are gaps I would put him/her in a different container until you get an escape proof cage.

For temporary storage I suggest a paper bag with a few pin holes for breathing. Put the snake in the paper bag. Staple or tape shut. Put the bag in the tank. Do not put it on the hot side. She/he may over heat and won't be able to get away from it. Unless you use a really big paper bag.

How big is your snake anyways?