Methods and non-volatile storage systems are provided for using compensation that depends on the temperature at which the memory cells were programmed. Note that the read level compensation may have a component that is not dependent on the memory cells' Tco. That is, the component is not necessarily based on the temperature dependence of the Vth of the memory cells. The compensation may have a component that is dependent on the difference in width of individual Vth distributions of the different states across different temperatures of program verify. This compensation may be used for both verify and read, although a different amount of compensation may be used during read than during verify.