Baz, if all you are doing is pulling the cooler, there is no need to drain the sump or remove the filter.
The pressure in a closed system has nothing to do with the heat. The heat comes from the heat rejected by the engine. A certain percetage of heat goes into the cooling system, some into the oil, some out the exhaust, and some goes to the atmosphere, through the walls of the castings.
If you are replacing the radiator, I'd flush the block out well with the strongest available flushing compound I could find. Accumulated deposits in the water passages will measureably reduce the ability of the heat from combustion to be transferred to the coolant, as the deposits essentially act as an insulator. If you're not replacing the hoses, inspect them carefully for any soft spots, or signs of collapse. Pull the water pump, and make sure the impeller is in good shape. Erosion of the impeller fins will reduce water flow, leading to higher than normal water temps.
What kind of temperatures are you normally seeing on the gauge, and is your gauge accurate?
Change the thermostat to a 180 degree version, if you haven't already.
Probably more than you wanted to know, but I don't have cooling problems on any of my cars, including the ones out west that operate quite often in 100 degree or better ambient temperatures.
The recommended oil, and my oil of choice, is Castrol 20W50. It's always served me well. There are several synthetics on the market that will work. I run Red Line 10W30 in my daily driver Volvo, and their racing oil in the race engine. Mobil 1, Valvoline Synthetic, Castrol Syntec, and Royal Purple are all good oils, as well.
Jeff