Readings & Meanings:
heat, summer heat, hot, HOT WEATHER
I hope you're doing well this summer. (Traditional phrase for the beginning of a "mid-summer card".
Kansai summers are hot and humid (sticky/wet/steamy/etc.).
Again, as in the case of 暖 and 温, the difference between 暑 and 熱 comes down to weather vs. touch.
暑 is for weather and intangible hotness. Just look at the kanji: there's a 日 (sun) bearing down over a 者 (person). The other kanji doesn't even have a 日 component! Easy!