1) You NEED a CPU cooler. Your case has very little to do with keeping your CPU cooler. The Heatsink and CPU cooler sits directly and top and account for about 90% of the cooling.
2) You don't need a case with loads of fans. One front intake, one rear exhaust, one roof exhaust is PLENTY. Once again, you do not need a FULL tower case, MID-TOWER is plenty big enough.
3) Capacitor ageing. Not true for modern day PSU's, the capacitors are much better quality. A 550-650w unit BRONZE RATED 80PLUS will keep you going for 5 years no problem. Corsair, XFX, SeaSonic are all recommend brands.
A CPU cooler (such as HYPER EVO or HYPER 212+) will only set you back about $25. Pair this with a $60-$70 case and your all sorted for under $100 leaving the other $60-70 to be spent on components that will make an active difference to performance, such as a better GPU.