Matt,
The way I have done this, and it seems to have worked well for my car is to move the heater levers to the full heat position. Then disconnect the heater hose from the firewall on the drivers side (after draining the fluid). Connect a small extra section of hose to the outlet on the firewall and point this downward. With the heater hose section still connected to the engine, put a small funnel on the end of the hose and slowly fill with new radiator fluid. Either get another person to hold up the funnel end while you pour, or you can tie it up with a small piece of wire. Pour slowly. Eventually the fluid will start to come out from the extra section of hose connected to the firewall side. Although, I have also had my overflow tank overflow before the other. Not sure why, but if the later happens, try to catch this before it happens. This means once in a while, look in your overflow tank while you are filling. Stop filling when the overflow is ~ ½ full.
Reconnect heater hose from engine to firewall. Start engine and let warm to operating temp. With a glove on, squeeze the large top radiator hose with your right hand. While holding the squeezed hose, use your left hand to pinch off the small hose connected to the overflow tank (use a flat smooth pair of pliers, ie. Needle nose pliers to pinch small hose). Now release the large hose while still pinching the small hose. You will hear the system suck water back. Do this procedure several times. You will notice the fluid in the overflow tank go down a bit. This means that the air is out. Sometimes it also helps to park the car on a slight incline, front higher than the back. The goal is to ensure that no air is trapped in the system. This extra air, can and will cause overheating, whereas the thermostat doesn’t work as designed with air trapped in the system.
Good luck!
Bob
bpossel
Memphis, TN.
1971 280SL
1997 E320