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Bulbs of the movie theater type are large high pressure xenon DC arc lamps. To ask what temperature they are does not make much sense. The arc itself is 600 K. The lamp envelope is quartz or sapphire and while it would certainly sizzle your finger, the temperature depends on the cleanliness of the bulb, the cooling airflow, the wattage, the type of lamp and the age of the lamp.
They are 15kW lamps. Imax projectors use 2 of them.
Each lamp produces 600,000 lumens. If you put a log in front of it, it would spontaneously combust...
Asking the temperature of the lamp makes a lot of sense. The 600k that you mention should be 6000k and is the colour temperature and has nothing to do with the actual temperature of the lamp whilst operating. It is merely the best way to describe the colour of the light when compared to the black body locus on the CIE Chromaticity Map.
The clear quartz glass jacket of the lamp has an operating surface temperature of about 1,300 degrees. To prevent the lamp from overheating, it has coolant "jackets" that allow cool distilled water to be pumped around the electrodes at a rate of a little over 30 litres per minute at about 100 psi. In addition, an exhaust fan removes about 34 cubic metres of air per minute from the lamp housing.
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