Oil in the coolant won't cause an overheat. What you have might even be some sort of sealer.

Oil mixes with coolant and turns brown.

Pump air into each cylinder ( piston at top, both valves closed ) the look for bubbles in the rad , level rising. This is a fast easy check.

With a cold rad and hot motor, you are losing circulation either from a stuck t stat or compression entering the cooling system. Don't just pull the stat, many have a valve on the bottom to block the bypass, at that point you will overheat.