It means "Here, the weather is just getting warmer and warmer."
Let me know if you need further explanation:)
Kochira dewa : "kochira" is polite version of "koko" (here, this place). "Kochira dewa" means here in contrast with other place.
kikou ga : "kikou" is climate. "Ga" is a particle for subject.
dandan: adverb. "gradually"
atatakaku natte: "atatakaku naru" is to become warm. "naru" is changed to te-form in order to connect to "kimashita".
ki mashita : literally means "come." It's used to express that some change started, and it has been kept changing until now.