To carb at room temp, you need to use a really high pressure. Here's a calculator to help you out:
For example. An average CO2 level for an APA is 2.7 volumes. If the keg is at 70F, it'll need 32psi to carb.
I would carb at the higher pressure, then disconnect the gas and chill the kegs. then vent off any excess pressure from the kegs and turn the pressure down to serving pressure (around 6psi) and reconnect them.
In the meantime just keep an eye on craigslist and the local yard sales for an old chest freezer or fridge. You just spent how much on a four keg kit, but you can't spend another $40 on a fridge?