Warm vs Cold Season is a little bit about how much of a sun beating a grass can take, but it's more about temperatures. A warm-season grass might survive the winter, but it'll turn green late and brown early because of the average spring and fall temperatures.
I understand that for a lot of the summer, temperatures in "warm-season" areas are only 5-8 degrees hotter than New England, but the spring and autumn temps have a much larger gap.
If you're looking for something to thrive, my advice is buy a seed mix. Scotts sells one that's a combo of Kentucky Bluegrass, Ryegrass, and Fescue. Whatever doesn't survive will be displaced by something that will.
Fescue is what's used for northern football fields. Kentucky Bluegrass and Ryegrass will soften up the mix. I have some patches of Bent Grass and Kentucky Bluegrass that do just fine in full sun, Zone 5a, with no treatment or watering (except in >2 week drought periods)
No grass will do well in full sun during drought periods if it isn't watered. Basic lawn sprinkler is $8, and you only have to break it out a couple times a month, and that's only if it isn't raining.
I have to do this so my three dogs don't polka-dot my lawn.
Summary: full sun cool-season grass, rather than warm-season. Scotts blend of Kentucky Bluegrass, Ryegrass, and Fescue. Water during droughts. Should be golden.
Alternative: you could always go freedom lawn. Just mow, and let the chips fall where they may. Eventually some kind of ground cover will move in. (As long as there aren't dogs dropping urea nukes - nothing survives that during a drought).