First of all, rabbits have a fur coat. This does trap some heat. While they do moult, they will are left with a fair amount of fur. Some moult later than others, so still have some winter coat later into the summer. This winter coat has an undercoat that this thicker and used to trap the heat more in the winter and insulate them against the cold.
Another thing to consider is that domestic rabbits come from Europe. It is not really that hot there most of the time. Over the many years they developed, it was simply better to have a thick coat to deal with the weather than risk freezing in the winter. While the thicker coat has been bred out of some breed, most still have it and some breeds have a thicker coat even.
Wild rabbits tend to live in burrows. The temperature is more consistent underground, staying cool in the summer and warm in the winter. If they get hot in the summer, they can just go underground to help stay cool.
Rabbits are most active around dawn and dusk. This tends to be when it is cooler, especially in the summer. They avoid the heat of the day if they can.
Rabbits have ears and use them to help keep cool. There are large blood vessels in the ear.As the blood goes through these, it gets cooled by the air before going back into the body. Elephants have a similar method of cooling. Breeds with smaller ears might have a harder time keeping cool compared to those with large ears in relation to body size.
Many animals do not handle the heat well.
Essentially, rabbits have evolved to live in a cooler climate. Because of this they have a fur coat that keeps them warm, but that means it is harder for them to stay cool when it gets hot. They do have some adaptions to deal with the heat as well.
