Halogen lights are actually designed to run hot, hotter than normal incandescent bulbs. Filament bulbs in general produce light by heating the tungsten wire to white heat but that means there is waste heat which makes them inefficient. There is also a limit to how bright they can be before the wire burns out because the metal evaporates. Halogen bulbs have a small amount of iodine or bromine inside which deposits evaporated tungsten back on the filament so they can be brighter and not burn out too soon. For that chemistry to work the inside of the “glass” (fused quartz not ordinary glass) has to be quite hot which is why the bulb is usually fairly small and burns you.
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