Someone invents a portable, incredibly high-powered laser or similar energy weapon. The mechanism of energy production can be hand-waved away. In other words, it will heat up. Lots. Gigawatts lots, or terawatts/petawatts/etc. Handwave any production rate you like into this.
Using only substances that exist in our real world, what is the practical limit on how quickly a portable energy weapon could be cooled-down? In other words, what is the maximum sustainable energy output of such a weapon, assuming cooling rather than energy production is the limiting factor?
The sort of thing I'm thinking of: Suppose you had a larger device nearby (on a truck, say) which could cool down helium to a liquid and pump it into your energy gun via a tube. The liquid helium would have to be pumped around quickly to prevent it from boiling. For sufficiently high weapon wattage, the sheer volume of helium needed, and the size of the cooling apparatus, would exceed what you can put on an accompanying truck. I suspect substances other than helium will have a better heat capacity before boiling, or a better rate of heat transfer, or some other property, but you get the idea.
Other than the internal mechanism of the weapon, there is no significant advance in materials or other technology beyond what we have here today.