Ramping pass voltage to enhance channel boost in memory device, with optional temperature compensation

A non-volatile storage system, comprising:

• a set of non-volatile storage elements formed in NAND strings on a substrate, including at least one selected NAND string selected for programming in a program-verify iteration and at least one unselected NAND string unselected for programming in the program-verify iteration, the set of non-volatile storage elements is in communication with a plurality of word lines, including a selected word line selected for programming in the program-verify iteration, and unselected word lines unselected for programming in the program-verify iteration;
• and
• at least one control circuit, the at least one control circuit, in connection with a program portion of the program-verify iteration:
• (a) configures the at least one unselected NAND string to allow boosting in at least one channel region in the substrate, below the at least one unselected NAND string, (b) steps up a voltage of the selected word line from a respective pre-program pulse voltage to a program pulse voltage at a step up time which is before a program pulse time period, and maintains the program pulse voltage during the program pulse time period, and (c) to boost the at least one channel region, during the program pulse time period:
• applies an increasing voltage to at least one of the unselected word lines, the increasing voltage applied to the at least one of the unselected word lines is increased at a rate which is a function of temperature.