i have worked on 5.3 and 4.8 engines ,changed waterpumps and thermostats never had an issue with trapped air in the sytem.like cowboy said run it with the cap off and usually the air purges its self out of the radiator.another method that i have used which guarentees no air is a device that puts your cooling sytem into a vacuum state,once the antifreeze has been drained out of the cooling system.once thats done then you would attach the coolant bottle to the device and its sucks all of the antifreeze back into the cooling system.works very well .you could still have a head gasket issue ,but normally the temp gauge will fluctuate when that happens and usually will boil over.another way to see if its a head gasket is to remove the rad cap once the engine temp is up and use a emission tester to sniff for combustion gases in the cooling sytem. hope this helps.

 

Do your radiator hoses get hot? If the issue wasn't there beforehand I would start by double checking what you did. Having no heat but an overheating engine doesn't match many possibilities, low fluid or air pocket are basically it unless you have multiple issues.