暑い, 熱い, and 厚い: heat, temperature, or thickness
The three words are all read あつい. Distinguish heat in weather or a room, the high temperature of an object, and physical thickness, while checking context in figurative or overlapping uses.
暑い: hot weather or surroundings
暑い is commonly used for heat in the weather, the air, or a room that surrounds a person. 今日はとても暑いです。 says that today is hot, while 部屋が暑かったので窓を開けました。 describes the heat inside a room.
A speaker who feels hot can also say 私は暑いです。 The focus is the sensation of being in hot surroundings, rather than measuring the speaker's body as a hot object, so 熱い is not used in this ordinary context.
熱い: an object has a high temperature
熱い is commonly used when something touched, eaten, or drunk has a high temperature. 熱いお茶を少し冷ましてから飲みました。 and 鍋がまだ熱いので触らないでください。 describe heat held by the tea and the pot.
It also appears figuratively in expressions such as 熱い思い for passionate feelings and 熱い議論 for a heated discussion. This does not make 熱い the automatic spelling for every emotional use of あつい; check the noun and the writing convention of the text.
厚い: thick or deep in degree
厚い describes the distance between two surfaces or a substantial layer, as with books, walls, and fabric. 机の上に厚い本が三冊あります。 and この壁は厚いです。 both focus on physical thickness.
It also appears in expressions such as 厚い信頼 and 厚い友情, where trust or friendship is deep and substantial. Even though all three words sound alike, 厚い本 is unrelated to weather or temperature. Use the noun and the wider sentence to identify the intended sense.
Quick check: Why is あつい written 熱い in 熱いスープを少し冷ましてから食べます?
Show the answer and why
The soup itself has a high temperature, and the sentence says it will be cooled before eating. Heat in the weather or a room would normally use 暑い, while the thickness of a book or wall would use 厚い.