Dr. Joseph Waligore has published online some of his what I see as very important research clarifying what the "Enlightenment Deists" believed in.
While almost all scholars continually assert that the God of the Enlightenment deists was a remote, uninvolved, watchmaker God that generated no love or warmth in people, none of these assertions are true. A majority of the deists thought God or the angels performed miracles; many of them prayed fervently to a God they adored; some even went into raptures of ecstasy at God’s wonderful benevolence. Some of them believed God or the angels protected people from danger by putting thoughts into people’s minds warning them of danger. Many believed the devil might perform miracles, and so any possible revelation backed by miracles had to be examined to be sure it was not done by the devil. A significant number of them viewed themselves as sincere Christians who spent their lives explaining where and why orthodox Christianity had strayed from Jesus’ simple message. A few were more interesting or featherbrained (depending on your perspective): one believed an angel had given him the key to interpreting prophecy, another said he received a sign from God to publish his first book, and another believed in reincarnation. Enlightenment deism was not modern secularism, or even a halfway house to it; the deists were preaching a religious alternative to orthodox Christianity that they hoped the world would embrace. Their piety and theology has been neglected, but it is due to our misunderstanding of it and not their theology’s lack of interest or influence on our culture’s intellectual history.
The entire article is worth a careful read. I’m not sure if I am comfortable calling this “Deism”: but Waligore’s point is that many of the folks we think of as “Enlightenment Deists" actually believed THIS. If it's proper to term this Deism, it's certainly a form of "Christian-Deism" as David L. Holmes termed it.