The weatherman said we should expect a warmer than average summer with some blisteringly hot days.

Skin blisters when it gets very hot, or is badly burned.  So, in this sentence, blisteringly hot means it could be so hot that it feels like a person’s skin could be badly burned.　

[氣象人員預測，今年夏天比往常還要熱，會有酷熱無比的日子。]

句中 a warmer than average summer 是「比普通夏天更熱的夏天」；blister若作動詞用，可指皮膚因受傷或過熱而起水泡（或氣泡），如今拿blisteringly hot來形容天氣，當然是「熱到不行」囉！