Welcome!
Mathematically, the rate constant is derived from Arhenius equation which hides a lot of constants in the A, but clearly depends on T in the exponent. The higher the T the higher the rate.
Conceptually, a higher temperature means the molecules are moving faster, which means they bang into each other more frequently and when they do collide they have enough energy to break apart their old bonds. If you like those humpy graphs, temperature supplies the energy to get over the hump of the transition state and into the products.
Is there something else you think ought to affect the rate constant?