Day two of New England's heat wave will be the hottest for some with most of New England failing to fall below 70° overnight and some failing to fall below 75°. Temperatures will climb rapidly into the afternoon, with highs topping out in the 90s for just about everyone and heat Index values reaching the 95-107° range away from the coastlines.

All of New England except for the south coast and the downeast coast. Rare (for New England) excessive heat warnings are up for portions of New Hampshire and Maine. In fact, the excessive heat warning issued for portions of Piscataquis and Penobscot Counties is the first such alert ever issued by the Caribou National Weather Service office. In order to get this alert in New England, heat index values need to reach 105° or higher.

Wednesday will be similar to Tuesday in regards to storm activity. That is to say that most areas should remain dry, but isolated storms will likely pop up in a few places in the afternoon and evening. Any storm that forms will be capable of becoming strong to severe with strong winds being the primary threat. With that said, coverage will be spotty with a general lack of forcing and a cap (a layer of warm aloft that makes it more difficult for storms to develop) in place.
WRF-AR2 showing potential weather this afternoon. Some mesoscale guidance is more excited about storm activity today than others, but given the current environment, we're leaning toward the lower end of storm coverage today:

Heading into Thursday, a cold front will begin to enter into the northern tier of New England for the afternoon. This will help cool the northern tier after a quick warm-up. For central and southern New England, it will be another hot day from beginning to end with highs well into the 90s and heat index values around 100° once again.
Coverage of thunderstorms will likely be greater than it was on Wednesday with a more favorable environment for development. The front will provide better forcing, shear will increase and the cap on Wednesday will be eroding away as the ridge begins to collapse southward. Storms will again be most likely across northern New England, with chances becoming lower as you head south in New England. With that said, storms can't be ruled out for anyone in the region, like Wednesday.

Along with the generally more favorable environment for storm development, it will also be more favorable for the development of stronger storms. Given the heat and humidity, there will be ample moisture, lift will be elevated as the front moves into northern New England, shear and instability will both increase as well.
CAPE values (a measure of instability) will increase to up to 2,000 j/kg. This indicates ample instability for storms. At the moment, severe storms don't look overly widespread, but any storms that form will be able to go severe given the environment. The Storm Prediction Center currently has southern Vermont, southwest New Hampshire and the western two thirds of Massachusetts in a "slight" risk (level 2 of 5) for severe storms. Strong winds and torrential rainfall are the biggest threats.
Storm Prediction Center thunderstorm outlook for Thursday:

Friday will see the cold front continue a slow push through New England. This will bring cooler weather for most of the region. It will still be warm, but not oppressively hot for most. In addition, an onshore flow looks to develop in the afternoon, which would aid in bringing cooler temperatures inland.
Coastal areas may actually begin to cool in the afternoon after a very warm start. The exception to all this may be Connecticut, which could see another day into the 90s as they will be south of the cold front and too far away from the cooling coastal influence. As for scattered storms, it will depend on the exact timing of the front, but at the moment they're looking most likely across interior southern and central New England with coverage becoming more isolated to the north and east.

The front looks to stall over New England for the weekend, setting up some sun, plenty of clouds and a few showers and storms around. A chance for more widespread showers and storms may come on Sunday afternoon through Monday as another disturbance moves to the north of New England, bringing its fronts across New England.
Weather Map for Monday morning, showing the disturbance tracking to the north of New England:

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