London/dispersion forces
When we lower the temperature of a substance, we are decreasing the average molecular kinetic energy (they're slowing down). As mentioned in the comments on the question, this doesn't really affect the electron cloud.

So, the substance has been cooled down and molecules are moving more slowly. At this point, it's not that the dispersion forces because stronger, but rather that they become comparatively stronger. While in the gaseous phase, the molecules have velocities of several hundred meters per second. At those speeds, London forces don't really have much of an effect. But, as the molecules are cooled and slowed down (this seems to suggest this is around 10m/s), London forces can cause more interactions between molecules. If the substance is cooled far enough, those forces are able to overcome the kinetic energy of the molecules and they condense into a liquid. As the cooling continues, the molecules move around less and less until they take on a definite shape, at which point it is considered a solid.

The primary issue with your intuition is merely understanding what cooling the substance down really does.