This is the 12067th most frequent Korean word.
높아지게
"To become higher" or "to rise."
Here, '높아지게' describes the process of the temperature increasing, emphasizing its becoming higher.
기온이 점점 높아지게 되었다.
The temperature gradually became higher.
In this sentence, '높아지게' is used to indicate the improvement of his skills, facilitated by external conditions.
그의 실력이 높아지게 환경이 도왔다.
The environment helped his skills improve.
'높아지게' in this case describes the uplifting effect of music on emotions, used metaphorically to indicate elevation or improvement.