Trying to sort color palette by heat

all.

My company wants to use our own internal styles for our heat maps. Therefore, I have a list of colors that I need to sort by heat (I have hex, rgb, and hsl values to work with). However, I can't seem to find any online color calculators or sorters that will help sort colors in this particular way. The colors I need sorted are:

#FEB01E
#EEC847
#90AB06
#70AD47
#81BE67
#2BA9AA
#527B6A
#3F678C
#72327A
#525252
#5B9BD5
#F27863
#F6B5A4
#FFEBBD
#C74C2A

Picture added so you can see the colors:

Colors to sort

If anyone has any ideas, I'm open to them. I tried to sort them a bit on my own, but I'm certain it's not correct. Any help is appreciated!

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