Hey maybe you (the OP) already know this, but I thought it was worth saying. Just to reinforce what russ watters said:
The seasons are not caused by a change in the distance between Earth and the sun (Earth's orbit is nearly circular)
The seasons are not caused by the fact that the hemisphere in question is closer to the sun due to the axial tilt during its warm season. The axial tilt causes a *negligible* change in the distance between that hemisphere and the sun (because the sun is so far away).
Simply put, the seasons are caused by the axial tilt, but for two very specific reasons:
The tilt means that in the summer, the sun is higher in the sky.
The tilt means that in the summer, the sun is up for a longer duration (the days are longer).
Regarding the first point, it is relevant because it means the flux being received (W/m^2) is actually larger. Draw a picture of a vertical "beam" of sunlight (that we interpret to contain a certain power) hitting the surface of the earth. Now draw a beam of the same width, hitting the surface at a very oblique angle (representing the sun being lower in the sky in winter). You will see that the same amount of power is spread over a much larger surface area, making for a lower power per unit area.
That is my understanding, anyway.