Success!!! That did it. I did as Phil & Diesel Friend suggested, filled the head and the radiator from the radiator hose. Then I let it idle for a few minutes with the reservoir cap removed, but I only saw bubbles while revving the engine.
I took it out for a longer drive this time and it only went above 80c while it was idling (I was adjusting the new headlight lens).
Thanks everyone for the suggestions. If it wasn't for forums like this, I'd probably be taking my cars to a mechanic even to check the tire pressure.