[mivayan]

I understand the effect of the scales but what does "Caellum prefers cold +3" mean?

The temperature scale ranges from heat3, to heat/cold0, to cold3. Most nations prefer heat0 and get -5% income from a province if the temperature scale there is heat1 or cold1, -15% if it is heat3 or cold3. Caelum prefers cold3, and only if the temperature in a province is cold3 will they get the normal income from that province. If the temperature scale in the province is heat0 they lose 15%, if the temperature is heat3 they lose 30%.

Should a Caelum pretender shift the scales towards cold +3??

Yes since you get income and supply penalties otherwise.