In early, out early - as Marshall says. There is likely to be nothing to gain by leaving peas on into the summer. You may well be able to enjoy peas again in the fall. Despite their ability to sprout in cool soil, don't be afraid to sow seed during the heat of summer.
A snow pea like Sugar Pod will grow fairly well as the temperatures begin to drop but they probably need to go in well before summer is on its way out. Growth will slow as the weather cools and they may even suffer some damage in the first frosts so it is best to plan on harvesting them about that time. I single out snow peas because you won't have to wait for the seeds to mature. Generally, they are quick to arrive in the kitchen and you don't even have to wait for the pods to develop! The flowering tips to the vines are delicious.
Peas are not the most productive of crops but you can get a lot out of the space if you have 2 crops coming off the same ground. And yes, you can grow and harvest peas, wait a few weeks, and plant peas right there again for the fall. That may make additional sense because the "work" to peas (other than shelling) is mostly in putting up a trellis. Make it sturdy because the vines will catch a lot of wind and if things get kind of topsy-turvy out there, the pea vines will grow that way and harvesting can be a mess.
Steve