Here’s a list of local cooling centers in RI:

http://www.riema.ri.gov/coolingcenters/index.php

And in MA:

Brockton: Cooling centers will be open through Thursday between noon and 6 p.m. at the community room of the Belair Towers at 105 Belair St. and the community room of the A building of the Campello high rise at 1380 Main St. Seating capacity is approximately 50 people. Food will not be provided.

Easton: A cooling center will open at Frothingham Memorial Hall, 15 Barrows St., from 4 to 8 p.m. It will remain open until Friday, July 6, from 8 a.m. to 8 p.m. If additional days are needed, an announcement will be made.

Foxborough: Cooling centers are open at the Foxborough Senior Center, 75 Central St., and the McGinty Room in the Foxborough Public Safety Building, 8 Chestnut St. The senior center is open from 8 a.m. to 4 p.m., but the McGinty room is open 24 hours.​