Should I run my heat lamp on a thermostat?

Yes — this is one of the few points of near-universal agreement across r/leopardgeckos, r/BeardedDragons and r/reptiles. Unregulated heat bulbs can overshoot basking-surface temperatures and have been linked in community threads to thermal burns and even bulb-related fires. A dimming (not on/off) thermostat is preferred for light-emitting bulbs because it doesn't flicker the bulb on and off, which shortens lifespan.