I haven't built an incubator, myself, but I hatch eggs - frequently - and I think I understand some of the important functional aspects of an incubator. Without seeing your actual unit, I'll have to make suggestions based on assumption...but a heating mat is, as you already intimated, less than ideal for incubating. I get 'working with what you have', though.
I saw that in
another post, you mentioned that you had a temperature spike of 50C (122F) with the eggs - which could be fatal to them. You already tried covering the unit with a blanket, which caused the temperature spike. If the incubator isn't already in a room that's not subject to drafts, I'd move it to one, as that may help limit temperature swings. Ultimately, though, it sounds like a more reliable heat source will be necessary to stabilize the temperature.