Broccoli (Brassica) likes cool temperatures and tolerates frost, but exposure to too much cold can make the plant develop a head prematurely. This prematurely developed head will be small, and the plant may be permanently stunted. In spring, the prime planting time is 1-3 weeks before your last expected frost date. Until then, set your plants outside on mild, sunny days so they can become accustomed to sun.
Your plants can handle a light frost after you set them out: Broccoli endures cold better than heat. If you love broccoli, plant it again in midsummer for an autumn harvest. It will taste wonderful, and the heads will be larger. In either season, watch plants for little leaf-eating caterpillars. Pick them off by hand, or spray plants with Bt (Bacillus thuringiensis) insecticide, such as Thuricide.