Unlike a few neighboring states, Connecticut is pretty universally dog-friendly and they have an impressive roster of dog-friendly hotels to prove it. If you're trying to beat the heat, check out a new city and grab a room. Relax in the cool air until it cools down outside enough to get out and explore more!
There are several noted dog beaches in Connecticut, including Jennings Dog Beach. While they are only allowed off leash during certain times of the year, it's still a great place to dip your toes in the water if you need to cool off.
Although there is a water-based tour offered at Seaport Village, there are others that will get you out on the water and cooling off, whether it's just a ferry ride or a full-blown tour.