By raising the temperature of the reaction mixture, the particles have more (kinetic) energy and so move around at a greater rate. This means there are more frequent collisions, due to the increased speed the particles are moving, and there are more successful collisions. This is because, for example, if the success rate was 1/3 and there was one collision there would be a 1/3 chance of it being a success. However, using the same probability, if there were three collisions then there would be a high chance that at least one of these collisions would be successful.
To sum up: (1) the particles have more energy and so (2) there are more frequent collisions and (3) overall there are more successful collisions.
(There are three marks available - but you only need to make two points to acheive all the marks!)