Just split the budget into three parts: the GPU, the case airflow, and the cooling upgrade. Pick a GPU that sits just below the high‑end curve, so you don't waste money on the extra 20‑30 % performance that most games never use. Then buy a case with at least two good fans and a tight seal – cheap cases often let air slip out, turning a decent GPU into a heat‑stressed wreck. Finally, if you’re on a tight budget, stick with a single 80 mm blower that pulls air through the rear and front vents, but if you can stretch a few bucks, get a small 120 mm AIO. That way the CPU stays cool and the GPU runs hot‑but not hot enough to throttle. In short, avoid the over‑engineered cooling for the sake of looks; go for the most efficient airflow for the price you’re willing to pay.

Sure, send over the part list and I’ll check for the usual heat traps. Just keep the list tidy—no extra cable loops, no hidden fan noise, and make sure the case has at least two intakes. I’ll point out the spots that could get hot and any overkill in cooling that could just eat your budget. Let's see if your rig will stay chill or start a sauna.