"There are many in this world who are wholly destitute of saving grace, who yet have common grace. They have no true holiness, but nevertheless have something of that which is called moral virtue; and are the subjects of some degree of the common influences of the Spirit of God. It is so with those in general that live under the light of the gospel, and are not given up to judicial blindness and hardness. Yea, those that are thus given up, yet have some degree of restraining grace while they live in this world; without which the earth could not bear them, and they would in no measure be tolerable members of human society. But when any are damned, or cast into hell, as the devils are, God wholly withdraws his restraining grace, and all merciful influences of his Spirit whatsoever. They have neither saving grace nor common grace; neither the grace of the Spirit, nor any of the common gifts of the Spirit; neither true holiness, nor moral virtue of any kind. Hence arises the vast increase of the exercise of wickedness in the hearts of men when they are damned. And herein is the chief difference between the damned in hell, and unregenerate and graceless men in this world. Not that wicked men in this world have any more holiness or true virtue than the damned, or have wicked men, when they leave this world, any principles of wickedness infused into them: but when men are cast into hell, God perfectly takes away his Spirit from them, as to all its merciful common influences, and entirely withdraws from them all restraints of his Spirit and good providence." (Jonathan Edwards, Restraining Grace a Privilege)
The damnable heresy being showcased here in Edwards is "common grace." This particular heresy is related to other heresies (e.g., common influences of the Spirit, restraining grace, denial of the Creator's control over His creatures).