"It is hot in the summer."
デ is for location of an action e.g. at the restaurant "レストランで" or by means of something e.g. with chopsticks "はしで". に is for at a time e.g. at 1pm "一時に" or going to somewhere e.g. go to the restaurant "レストランに行きます" So you might be able to use the time form of に for in the summer, but not で. In this example they have used なつは instead of なつに to highlight summer as the main focus of the sentence i.e. in SUMMER I do a thing as opposed to in Winter.
When you use に as a particle, ___に is an adverbial phrase (a phrase that behaves like an adverb). なつに would be used for sentences such as "I [verb] in/during the summer", where "in/during the summer" is the adverbial phrase. なつは would be used for sentences in which you are describing the summer, such as how hot or dry it is.
I believe either should do. 夏は indicates minor focus on the topic 夏 (が would indicate more focus, or a transition to it when the topic of conversation was something else before). に identifies it as a time during, which in a simple sentence like this is basically the same thing.