Glass is a very poor insulator, and you'll be losing loads of heat through that mesh top.
All the glass enclosures I have, I've made plywood lids to replace the mesh. Paint them black and you hardly notice them.
As for the glass, try an insulating layer of foam or polystyrene. There's a product called 'abelflex' aka expansion foam. It's used in concreting and bricklaying to allow expansion and contraction where concrete slabs/panels/blocks or bricks join. You can buy this stuff in rolls and sheets of various sizes and also with adhesive backing on it. That would be a perfect way to quickly add some insulation. My local Bunnings only has 100mm rolls with the adhesive, but you can get larger adhesive rolls from concreters/bricklayers suppliers, probably even plumbing outlets.