Here's my balance ratings;
Damage - S; This sounds like an even stronger ion beam
Cost - ?
Surface area - S; Roof turrets are overpowered, plain and simple. Part of the balance right now is finding space for both weapons and defense on the surface of your ship, and this gives you weapons for free
Logistics - B?; The actual powering of the weapon would probably be easy, it's only B instead of A because of the overheating thing, which would turn it more into a gatecrasher
Range - SSS; The longest ranged weapon in the game right now is 9+ accelerator rails and EMPs tied at 600 meters. This would immediately become the goto, and really only viable kite weapon
Overall this sounds so ludicrously overpowered that it would make meta knight in brawl look like olimar. It would turn the balanced and diverse meta we have right now into "roof turrets go brr"