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Temperature itself does not have any effect on ESR. ESR is often represented in the mathematical relationship:
ESR = DFXc = DF/2πfC (Formula 1)
Temperature does affect capacitor performance. The temperature characteristic of the material defines the maximum rated operating temperature of the capacitor. For example, a X7R is defined to operate up to 125°C while a X5R is defined to operate up to 85°C. The total temperature of your circuit environment plus the self-heating (i.e. ripple current) of the capacitor combined cannot exceed the maximum rated temperature of the capacitor. For an X7R, if the circuit operating temperature is 100°C, the ripple current cannot introduce more than 25°C of self-heating.
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