Technically, mathematically, any thing above 0K (absolute zero) emits black body radiation (with the exception of black holes, which absorb any radiation the singularity at their center might emit, but I digress). Even the inside of your deep freezer, which is around 255K, technically emits black body radiation, including visible and UV radiation. But the amount emitted is so incredibly small that your eyes cannot detect the visible portion of it. The cooler something is, the less black body radiation it emits, and therefore the less UV it emits.
A tungsten bulb is a black body radiator. Most of its radiation is in the IR and red regions of the EM spectrum, with a little bit in the UV. A halogen bulb, because it is hotter, emits a bit more UV. But the amount of UV emitted is quite low.
Fluorescent bulbs require UV to work, and emit more UV than a tungsten bulb, even though they are cooler, because they are not pure black body radiators - they are discrete spectrum radiators superimposed on black body radiation, and it's the discrete spectrum from these (the blue and UV) that is down-converted by the phosphors coating the tube into visible light.
I wouldn't worry about tungsten or halogen bulbs emitting too much UV to affect your chemistry.