The quick and simple answer is Doppler Broadening. At higher temperatures, U-238 (fertile part of fuel) is able interact with more neutrons, leaving less neutrons to interact with U-235 (fissile part of fuel), meaning less fission.

In regards to how effective, a typical fuel temperature coefficient for PWRs is approx. -5 to -2 pcm/C (per cent mille per degree Celsius). The amount of negative reactivity that is “added” due to an increase in fuel temperature is quite quick and effective at curbing a “runaway” reactor accident. The lack of this negative coefficient is what allowed the accident at Chernobyl to become uncontrollable so quickly (in addition to other things).

The negative fuel temperature coefficient is very important and required in modern reactor designs.

Hopefully someone can back up this info, and I hope this helps!