게 불타오르다

blaze up, catch fire

불타오르다 is bursting into flame, and in these lines it is almost always figurative heat — a topic burning up social media (현재 SNS 상에서 뜨겁게 불타오르고 있는), a crowd's cheers (관객들의 환호도 뜨겁게 불타올랐습니다), a stock market running hot (주식시장에 이렇게 불타오르는 거). The adverb is usually 뜨겁게 "hotly" or 엄청나게. It is a heightened, dramatic word, and these lines are commentary and reporting rather than casual chat.

Register: heightened, commentary