I wonder if it's worth screening off the sides and back of that glass. For a start, being that open might be quite stressful to the snake, hence why he prefers the heavily covered side, but also glass is fairly notorious for heat loss

You can get decorative backdrops for snake vivs and glass terrariums that look like jungle landscapes, or even something as simple as black paper could do the trick. I know they run a bit more expensive but the specific vivarium decor backdrops are usually fairly resilient material that can be washed/disinfected so can be mounted in the tank - that'll probably also be the best bet for heat seeping through the glass if there's a fabric type barrier in the way of that

if you do decide to do that I'd recommend using a non toxic/non odour based sealant to stick it to the tank. Don't use sticky tape on the corners as it'll last about 5 seconds. If you do mount inside it'll also be worth running the same sealant around all the edges to again help it stay there but also to close off all edges and prevent water and other muck getting in behind the decor

this is also potentially a much cheaper option than investing in more heat, so IMO is worth a try before anything else