bleeding the cooling system

i changed the water pump and the thermostat so im thinking it has a lot of air in the system now, i did some searches on the forum and one said you could just warm the car up and leave the cap off (which is what i was doing earlier sense i saw a lot of air coming into the reservoir

is this an ok way to do it?

my radiator was still ice cold, and my air was still blowing cold (had it on heat full blast) when the car was at normal operating temperature (when i shut it off)

My cavalier will blow cold air when it is on heat if it doesnt have enough antifreeze in it. You might try adding antifreeze or checking to make sure you have the right amount in it.

yes, leaving the cap off is an ok way to bleed the system.