Answer: It is not the warm air temperature that causes broccoli to bolt (or flower). It is the warm soil. Add mulch and keep your broccoli well watered (check an inch down into the soil for moisture level), can help keep your plant going longer. I also careful watch my plant when it is producing a head. You want to make sure the plant does not flower, so cut the head before it has a chance to. Most varieties produce side shoots, so you will still be in the game.
To learn more about growing broccoli, check out my experience with growing the packman variety this season.