In a non-volatile storage system, one or more substrate channel regions for an unselected NAND string are boosted during programming to inhibit program disturb. A voltage applied to one or more unselected word lines associated with at least a first channel region is increased during a program pulse time period in which a program pulse is applied to a selected word line. The increase can be gradual, in the form of a ramp, or step-wise. The boosting level of the first channel region can be maintained. The increase in the voltage applied to the one or more unselected word lines can vary with temperature as well. Before the program pulse time period, the voltage applied to the one or more unselected word lines can be ramped up at a faster rate for a second, adjacent channel region than for the first channel region, to help isolate the channel regions.