You can put that lamp more in the middle of the tank if it helps. I used to do that, and if it's a mesh lid cover the screen with tin foil a bit.
But you NEED a thermostat to regulate UTH. Burns will happen otherwise. To me, this is a non-negotiable piece of equipment.
Check out amazon, look for Jumpstart Thermostats. Pretty inexpensive and can ship quickly.
You also need a digital thermometer with a probe secured to the bottom of the vive to measure the UTH. How else do you measure the UTH? You mention checking it... but how? Unless you have a handheld digital laser, I don't understand...