I would recommend scratching the lamp, and just going with your UTH. If more heat is needed, I would work on heating the room around the cage; this is what I do.
They do need to be seperated, as the others mentioned; it is a good indication though, that you want to buy another cage; but 100g is way too big for even the largest BP!
To save money, your best option would be to go with rubbermaid or sterilite containers; MUCH lighter, cheaper than tanks. But if you insist, satisfactory BP keeping can be done using tanks; I use them for all of mine, but there could be a whole book written on the extra requirements of doing so. (for one, humidity needs to be retained during shed times with plastic wrap over most of the lid.. they are heavy to lift when cleaning/hosing out is needed, etc.)