Actually, the amount of energy associated with the remnants of Chantal is quiet low - which is one of the reasons why the probability for redevelopment is also quite low. But never-the-less you have asked a good question. The warming of the land during the day is what drives the sea breeze and, as the remnants have drifted north, a high level of tropical moisture has moved north over the land masses that you mentioned (when one thinks of the tropics or the sub-tropics its hard to conjure up an image of even higher moisture content - but it indeed does happen). The higher precipitable water values along with the heat of Summer and the sea breeze interactions all produce a higher than normal concentration of daytime convective activity that declines in the later evening hours as the heat source is lost and the atmosphere stabilizes.
ED