How does rate constant change with temperature?

As a 'Rule of Thumb'. thehigher the temperature, the faster the reaction. Hence the Rate Constant increases.

Conversely for decrease in temperature.

See the Arrhenius Equation.

k = Ae^(-Ea/RT).

Where

k = Rate constant

A = pre-exponential constant

'e' = the exponential number ( 2.7818...)

'-Ea- - negative activation energy

R = universal gas constant

T = absolute temperature (Kelvin)

The last three terms are raised to a power of 'e'.