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Translating temperature values to RGB plot in C++

Hi all

I have a question regarding how to translate a single value into a RGB color, I'm currently programming i C++ under the Win32 API if that offers any help.
The value is in the range 0 to 5000, and I would like to represent the values as a gradient starting with black representing RGB(0,0,0), traversing through blue, red, yellow and finally white representing 5000 with a RGB(255,255,255).
I've tried several things, but with little/no luck.

Best regards Martin
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