These results are for a plane with half the fuel load that had it's radiators wired shut for the tests for less drag. It wasn't the standard way of measurement. There was no way to manually shut the radiators on the MkIX once it began to open as temperature rose - that started already 10 celsius over normal pressure.
Isegrim, you'll be pleased to hear Neil has got hold of the cooling figures for the Spitfire at 25 lbs on climb.

What they show is that the radiators do not have to be wired shut, under normal conditions they will be shut throughout the climb, as temperatures will not reach the level at which the radiators open.

This test was done at a sea level temperature of 8c (standard sea level temperature drops 4c with an altitude increase of 2,000ft)
As you can see, with the radiators shut, the coolant temperature climbs to a maximum of 106 centigrade.
The Spitfire radiators open when the coolant temperature reaches 115 centigrade.
So, at 8c, the radiators will not open even after a maximum power climb from 2,000 ft to 32,000 ft. In fact, it doesn't even come close to opening the radiators.
This chart also answers another question, Isegrim. The "standard summer temperatures" used in calculating the radiator suitability. The temperate summer temperature assumed in the standard is 27c at sea level, and the tropical summer temperature standard is 41c. Pretty high, but then the usual RAF practice of wiring the radiators open for climb tests shows they were interested in finding worse case numbers, not artifically inflating results.
Re: Wired shut radiator flaps - looking at some docs that 'may' suggest this was not needed to obtain the 5700fpm @ 0-5000ft.
No, looking at the cooling results, under normal conditions they would remain closed of their own accord.
These results were at 8c. Perhaps someone better at maths can work out likely results at higher temps?
The formula used in the tests was:

The value of Tn was 125c for full power and 115c for cruise.
Although even the RR tech guy I spoke to suggested that figure seemed high, maybe obtained with a 'cold' engine at the start.
I don't think they'd have run a full power test with a cold engine, or even taken off with one, for safety reasons. But you can see here that the coolant temp at 2,000ft at the start of the test was 78c. The report says that high speed radiator suitability figures are the temperatures reached after 5 minutes at full power in level flight.
Radiator suitability 1.36 = 125 - 21 / (coolant temp - 2)
coolant temp = 78c
(radiator suitability 1.36 at 3,000 ft level flight radiator closed, 125c max permissable coolant temp, 21c standard summer temp at 3,000ft, -2c observed temp at 3,000ft)
So 78c is the temperature reached after 5 minutes flat out with the radiators closed at 3,000ft. The climb test started at 2,000ft, but the start temp of 78c should still be very close to maximum in level flight at that altitude.
Yup I have seen climb rates closer to your 5080fpm 0-5000ft.
I suspect that's with radiator flaps wired open. The RAF usually tested with flaps forced open, to get a worst case figure. Of course, in real like the flaps didn't open until the temperature reached 115c, and cooling was pretty good even with the radiator flaps "shut" (shut on the Spitfire was about half the exit area of open, the flaps couldn't close completely)
Edit: This assumes my maths is right, and that's a dangerous assumption at this time in the morning
