Reading and verify operations are performed on non-volatile storage elements using temperature-compensated read voltages for unselected word lines, and/or for select gates such as drain or source side select gates of a NAND string. In one approach, while a read or verify voltage is applied to a selected word line, temperature-compensated read voltages are applied to unselected word lines and select gates. Word lines which directly neighbor the selected word line can receive a voltage which is not temperature compensated, or which is temperature-compensated to a reduced degree. The read or verify voltage applied to the selected word line can also be temperature-compensated. The temperature compensation may also account for word line position.