It's is because गर्मी is feminine. It is not connected to the "they" because the को in the sentence (उन्हें = उनको) blocks the subject and makes the verb match the object
Why do they use लगती with "they"?
Based off of a previous post it seems to be because the लगती is referring to the ठंड which is feminine.
I think it's because "they" is assumed to be feminine... But I don't see why लगते is not accepted because the sentence doesn't seem to indicate any gender otherwise.
I guess if it's an all female group it's लगती, else it's लगते