Yes it is very difficult to cool 5 Kw of power in 12 meter long airplane flying hundreds of kilometers per hour at high altitude where temperature is -40. Akinci needs more than just small opening where cold air can get in at high speed.... Akinci needs a complete redesign to carry a radar. It is almost impossible for Baykar to accomplish this...
As a comparison, a $100 consumer grade computer CPU cools about 50W/cm2 with $20 heatsink and a tiny fan in a 5kg case, while a 5kW radar (500-2000cm2) would need 2-10W/cm2 cooling in a 6 ton air-craft. It really does not sound like an impossible problem, specially since the radar is made out of high efficiency GaN with excellent thermal properties while the CPU is made out of silicon which stops working around 100C.
Even worst, you think someone capable of designing complex power-electronics and air-craft will not be able to design a cooling solution for mere 5kW?
Had you been talking about 1.21GW for a flying Delorean then I would have understood you but even fully passive cooling of power electronics operating +20kW is done all the time in cheap consumer products.
So no,
it will not be impossible for Baykar or for any other air-craft which
already have such radar to accomplish this.
Also, "12 meter long airplane flying hundreds of kilometers per hour at high altitude where temperature is -40" is a positive for cooling as you have large surface area and high air-flow of cold air.