"Hot Light" is a slang term for studio lights that used Tungsten, Quartz or Halogen bulbs that are continuously on rather than triggered like a flash. These lights got their name from the amount of heat that would be produced from them during use. Though some hot lights are still difficult to use in a studio setting due to heat (food photography for example), many companies have produced very efficient hot lights that are able to stay quite cool in all but the most extreme conditions.
Hot lights have been used commonly in videography for many years. Now that digital cameras are gaining popularity, hot lights are getting popular in still photography again as well.
The main advantage of hot lights is the fact that they are constant. This means that what you see through the lens during composition is what will be captured when the release is pressed. This is a tremendous advantage for beginners as they learn to see what effects come from placement of lights as it happens. It also reduces some cost due to the tendency for hot lights to be less expensive and the elimination of the need to have a flash meter.
Common objections to hot lights, aside from the potential heat that they generate, is the difference in color temperature and the amount of light they are capable of producing. While most studio strobes and monolights are balanced for upwards of 5200K (daylight), most hot lights are only capable of producing warmer light in the range of 3200K (tungsten). This difference is significant for film photographers because it requires them to correct the color balance with filters or shoot with tungsten-balanced film. In addition, the amount of light produced by a standard hot light is typically less than that of a studio strobe. In simple terms, this means you will be limited in your selection of apertures and shutter speeds since less light is available during exposure.
Many beginners use work lamps or household light fixtures while they learn. These lights can be considered hot lights, but extra care should be taken when using them in the studio. In particular, these lights are not designed to be in contact with light modifiers or backdrop materials. Take precautions and have a fire extinguisher nearby if you decide to use work lamps for photography. Never leave hot lights unattended.
There are advantages and disadvantages to using hot lights in the photo studio. For digital photographers, many of the disadvantages become less significant. Choosing which type of light is for you depends on your level of experience, your medium, your subject and your style.