You say the temperature rose to just under the red line. What is that? 200 F is not overheating.
Purchase an infrared thermometer from Any parts store for $20. When the engine is at operating temperature, shoot the thermometer at various places around the engine - in particular the T stat housing, upper rad hose at radiator, top of radiator, bottom of radiator, temp sending unit, etc.
You'll see what's normal for your engine.
Carry the tool with you and if you think its overheating again, shoot the temps in all the usual places to verify what the temp actually is.
My engine runs at 180 all the time with a 160 T stat and 4 lb cap. When the dash gauge says 180, the top of the radiator and water outlet read 179-183. Bottom of ther radiator reads around 154 or so most of the time.
This truck came to me with an overflow tank installed and I opted to leave it. This way I can fill the radiator all the way to the top. The plastic tank level goes up when hot and down when cold. They are available from any parts store or Rock Auto.
I('d also buy a new zero pressure or 4 lb radiator cap if you are unsure of your current cap's efficacy.
1950 Chevrolet 3100 (Ol' Roy)
1939 Packard Standard Eight Coupe (The Phantom) | 1956 Cadillac Coupe de Ville (The Bismarck) | 1964 Ford Galaxie 500 coupe |1966 Ford Mustang (Little Red) | 1969 Pontiac GTO (The Dishpit) I 1979 Ford F-100 | 1976 Ford F-150 (Big Red) | 1995 Ford F-150 (Newt)