Best way to beat the heat in summer is to head to your nearest water hole and jump in! For small kids I recommend Lake Shaftsbury State Park with it’s wide sandy beach suitable for castle building, large shallow end, and snack bar. Nice facilities, picnic areas, boat rentals, and grills. Fee charged. No lifeguard.
For later in the summer as things heat up, you may prefer Lake Paran in North Bennington. This lake is deeper and stays refreshingly cold. A small fee is charged. Snack bar, facilities, and a lifeguard. For a more adult experience, my favorite spot is the Dorset Quarry on Route 30 in Dorset. NOT for children, this very deep quarry is ringed by cliffs and is an amazing, beautiful place to swim. No facilities, no conveniences, and no charge.
Another place to cool off is in the Roaring Branch River, on Route 9, east of Bennington. Park along the highway (on the south side, or your right coming from Bennington), after you see the sign for the National Forest. A series of informal trails lead to a number of shallow swimming holes along the river. River temperatures range from frigid in the early summer to cold in the late summer. Not for very small children, but a fun experience for elementary age children with adult supervision. This is on National Forest lands and there are no facilities, no fees, and you are expected to pack out whatever you pack in.