He speaks literally and figuratively here. In Alabama all summers are hot. But, he mainly means that the summer is going to be full of protest, violence, and the "Roman Carnival" atmosphere because of the Tom Robinson trial.
This has been foreshadowed since the first page of the novel, when Scout/Harper Lee talks of how hot the town is in the summer. Usually, summers are lazy in Maycomb. No one ventures out in the heat. But the Tom Robinson trial will bring in people from Old Sarum and other neighboring towns, causing tempers to flare.
The literal meaning of ‘the summer’s going to be a hot one’ would simply suggest hot weather, but clearly that is not what Atticus is getting at. Aunt Alexandra and Atticus agree (although Scout is not convinced it was Atticus’ idea) that she ‘should stay ... for a while’ and in Aunt Alexandra’s words, addressing Scout, ‘it would be best for you to have some feminine influence.’ When the children meet Atticus, he starts to tell them that ‘We felt it was time you children needed –‘, but his justification for her visit is not answered directly. The reader already knows that Atticus has been absent on business for two weeks and that he is defending a case for a Tom Robinson, a black man, which is already causing tension between the Finch family and the white residents of Maycomb. Therefore the ‘hot summer’ Atticus is referring to is both the support his family will need during these difficult months and Aunt Alexandra’s preoccupation with bringing the children up properly.