When you replaced the radiator did they put in an aluminum one or a stock plastic one? The E36 and E46 had plastic radiators which were prone to failure. Their are aftermarket ones made out of aluminum that are much better. What temperature rating is the thermostat? I'm sure you have checked the coolant level? The level being low is usually the most common overheating problem. Air in the coolant system is the second most common. Double the check the level and bleed the system just to be sure.
Now is te car itself overheating or is te temp gauge shooting up? A way to find out is to turn the ignition on, but not the engine. If the temp gauge shoots up then the temp sensor is bad. Otherwise it may be your thermostat. Also check all your hoses for cracks, rips, tears to make sure their not leaking. Their is a lot of hoses that make up the cooling system of the vehicle, not just the upper and lower rad hoses.