Because PV=nRT. This is a formula from chemistry, also known as the Ideal Gas Law where:

P - pressure

V - volume

n - number of moles of the gas (where a mole is Avogadro’s number of molecules of that gas)

R - Boltzmann’s constant

T - temperature

So in a closed environment like a tire, the volume and moles of gas are constant. That means if the temperature goes down, with everything else being equal, pressure has to go down as well. Similarly if temperature goes up, then the pressure would necessarily have to go up.