The amount of heat in the atmosphere at any point doesn't really matter all that much for global warming. What matters is the break-even point between the amount of energy we gain from and lose to space. Since the earth emits more energy if it's warmer (black body radiation), the break-even point relates to the temperature of the earth. If we change something about the earth's in or output of energy, the earth's temperature will naturally rise until the break even point is reached again.

By introducing greenhouse gasses, we are affecting earth's ability to radiate energy to space and thus the temperature at which we have our break-even point. Should all greenhouse gasses disappear, the earth would rapidly start cooling until it reaches its new break-even point.