Of course, all radars of this type are pulsed radars. Continuous wave fire control/illumination radar has no relevant to this discussion. If we do some brainstorming with few rules of thumbs that we know, then this is what we get-
GaAs HPA (high power amplifier) can achieve power added efficiency (PAE) of around 40%. And GaN HPA can achieve PAE of around 50%. However, given there are others elements consuming power on T/R modules, such as switching circuitry, module control circuit, etc, overall module efficiency becomes much lower than PAE of only GaAs or GaN amplifiers, according to this paper.
Let's say if Aselsan achieved some 50%+ efficiency of its GaN amplifiers,
then overall T/R module efficiency could be reasonably around 33%.
So now, if MURAD wants to operate at 300KHz PRF then it means, it will draw some 10.3KW power assuming 1 microsecond pulse width. That means around 6.8KW turning into heat waste. And we know that MURAD's liquid cooling system is capable of 4.5KW cooling. If we left out 1.5KW for back-end hardware like estimated with APG-83 in the paper above, then 3KW cooling capacity is left for the array. So, now MURAD has to operate at less then 150 KHz PRF. And if it wants to emmit wider pulses (like two microsecond) then PRF is slashed further by half.
Maybe they can increase the cooling capacity with further updgrade potential as you said before. Or could it be that F16's 5.5kw air cooling capacity remains unchanged with Ozgur program along with built-in 4.5kw liquid cooling system of MURAD? Could it work like that? I don't know.