Firstly, do re-read the radiator tutorial in light of below. (I presume you mean that by "the guide")
Secondly....if you were off by 25% (I presume the radiator temp gauge at 25% of travel, not 25C) did you do the full preflight checks? Usually you should not do these until the radiator gets to 60-70 degrees which is just about 20% around the gauge. By the time you finish these properly the temps should be around 90c.
..around 33% of the gauge.
If not, do you know what mechanical reasons there may have been behind this? Did you check the oil and water before the flight and were they full? These are persistant between flights.
Did you run at normal mixture or lean?
What were the oil temps and pressures during the flight? They should give a clue as to what happened.
How long since last overhaul?
Also, when the temps started to climb, what corrective action did you take? If oil pressure drops a Merlin will last barely 60 seconds. What was your oil pressure when the engine quit? If you boil for long you deplete the coolant and make overheating worse..this affects oil pressure.
Ok, now you say you climbed at 180mph at 1/3 throttle open, so you were using very low boost, high RPM which is NOT at all what the Merlin likes. "Low revs high boost will bring you safely home to roost". 1000 - 2000 fpm is far to low a climb rate. She will do twice that and is designed to do twice that down low. What you are doing is effectively putting a car up a hill in fourth gear at very low speed with it kicking and complaining, rather than changing down and adding more throttle. You are stressing the engine constantly.
So, in summary, the way you have described the flight and subject to the questions above, I would have expected pretty much what you are saying. I suspect you may have started with depleted coolant and maybe too little oil as well. Surely this can't be realistic performance? Well, in a mishandled Baby Spitfire it most certainly can....
The Merlin MUST be flown to the published numbers or you will have trouble. Wet Nursing it will buy you just as much trouble as running it too hard.
OK, just tried your setup...best I could get the radiator up to was 110C on a perfectly new aircraft (two hour's flying on the airframe.) I must say too that those speeds, boost settings and climb rates are a devil to fly at... the Spit quite obvioulsy does not like them. I could not hold 180mph and 2000fpm climb with 1/3 throttle open but with 1/3 of boost gauge (about -1, -2, ) I could. Even so, my guess is certainly some pre-existing problem.
In general, get high fast, level off, cruise fast and if a temp problem reers its head, deal with it fast. By the time the temp gets to 130C (and remember the gauge LAGS the actual temp in the engine), your are well on the way to trouble. ALL performance figures and maxima are subject too
the overriding need to stay within maximum temperatures.