Since Maine is in the North of the United States, rest assured that you are not going to be seeing that much hot weather. With cold beaches at your disposal you might as well make the best of the situation and scout for the one that suits your mood. You should try the beach near Bar Harbor, while you will not find sandy beaches here, the rocky environment will leave you captivated.
You can always hike to the remote areas where you will likely have a shoreline just for yourself. The Acadia National Park is a good place to start from.
If you are somewhere around Bangor then consider travelling to Penobscot River Corrider, as this area is remote. There are a vast number of undeveloped shorelines which can be very pleasant for people looking for some peace and quiet.
If you want to find a location near the central coast of Maine then visit Holbrook Island Sanctuary on Cape Rosier. The best feature of this place is that while it is remote is still has decent parking, this makes it possible for visitors to come to the area on their vehicles without having to walk or hike.
If you live on the southern Maine coast, then your destination should be Cape Neddick Beach. However, if you are looking for a sandy location then you should visit Ferry Beach State Park. You will definitely find some nice peace and quiet at this beach.
Living near the coast lines puts you at an advantage but if this is not the situation in your case then you should consider freshwater lakes. Sebago Lake State Park in Casco and the Range Pond State Park in Poland Spring are some of the locations which should be on your radar as they have large sandy beaches.