I believe that you're going to want a desktop CPU to go with a small motherboard rather than an sTR4 behemoth. Coffee Lake refresh (e.g.: i9-9900K
) runs pretty hot. Intel has cranked up the thermals as they have pushed Ye Olde 14 nm process about as far as possible. I'm going to suggest one of those brand-new Ryzen 3000 series CPUs. You should be able to get plenty of power with a socket-AM4 processor that will fit on a small motherboard (assuming that you're able to fit in a graphics card using a 90° PCIe riser).
Micro-ATX is 9.6"x 9.6" and has up to 4 PCIe slots.
Mini-ITX is 6.7"x 6.7" and has just one PCIe slot.
I'm guessing that the front grille opening is about 7½" square. This isn't a standard form factor for PC cooling kits, but there could be an off-the-shelf automotive part available.
A pair of 2x92mm
radiators might fit in there side-by-side, but I'd rather listen to one 180mm fan than four 92mm fans.
1: i7-9700K, NH-D15, Z390M Pro4, 32GiB, RX Vega64, ½TB 960Pro +2TB MX500, Define Mini-C, SSR-850PX, Dell S3220DGF + LG 32UD99, RK9000V2-BR
2: R5-3600X, Hyper 212Evo, B450M Steel Legend, 32GiB, RX5500XT, 2TB SX8200Pro, P160, SS-660XP2, TV, G610