Tom read that on January 1, Earth is slightly closer to the sun than on July 1. Why, then, is it colder in January

than in July?

There is no "why", because it's not. It's colder in January only in the northern hemisphere, but in the southern hemisphere, January is early Summer.

The seasons are the consequence of the non-perpendicularity of the Earth's rotational axis relative to the plane of Earth's orbit ... the so-called 'tilt' of the axis. The variation of Earth's distance from the sun has very little to do with them.