I'm not going to dare attempt to multi quote at this point. LOL
Couple things:
1) Earth dog was correct, most modern homes have 15 or 20 amp limits
per circuit. So @ ~120V that's about 1500W or 2000W potentially max. As I said, that's per circuit (think your circuit breaker), however, unless you're plugging in your computer in your kitchen on your fridge/oven circuit, you're basically going to have 90+% of that top limit available to your computer.
The point is, with a 500,750,850 watt power supply, don't even give it a second thought whether or not you can pull that much wattage from the wall - you can.
2) Now, more importantly, I didn't need to read past "cheap" in your PSU description to reach this conclusion, but when I made my way to "ebay" it affirmed my feelings
-->Take your PSU out back and shoot it. Never skimp on power supply, EverEverEver. Go grab yourself an EVGA unit at whatever wattage you need + some overhead (extra) so that you can rest assured you have a quality power supply that will deliver everything you need without cooking your entire computer and razing your house down - if you don't take that PSU out back, it'll take you out back sooner or later.
3) Just to touch on your concern with the PSU pulling in hot air - I don't know why it hasn't been mentioned, but if your case is tall enough (read: the legs give it enough lift off the ground for airflow), just flip the PSU over so that it intakes air from outside the case (ambient instead of hot internal air). This will help keep the PSU as cool as possible
Edit: Make sure the case has cutouts below the PSU for this airflow option first, but any case worth it's salt does.
Best of luck to you! And remember, NeverNeverNever skimp on power supply!