Although broccoli plants themselves are extremely hardy, they don't handle big temperature fluctuations very well. Warm daytime temps followed by a few nights that fall below 50° may cause broccoli to "button up," meaning the plants will flower prematurely, forming tiny heads not much bigger than a single floret.
Any major stress—drought, a period of extremely cold/wet/hot weather, nutrient deficiencies (especially nitrogen)—can cause buttoning. (Some varieties do better than others under what the seed companies call "adverse conditions." Check the descriptive blurb on yours.)
The old-timers always said to wait until the weather has "settled" to transplant broccoli. In your area that's probably in early May, when spring's wild temperature fluctuations have flattened out. Here in central New Hampshire, I usually wait until the second week in May to put mine out.
Alternatively, you could cover your plants on nights when the temperature is forecast to dip below 50° .
Give your broccoli space in some deep, rich soil with a thick organic mulch for best results, and (if you've chosen a variety known for good side-shoot production), your plants should keep yielding over a long harvest season.