I'm not sure what you're after, nuget102. I didn't try to relate a no pole world with reality at all, although you could see it as representing such a small part of the world that there isn't much of a difference across it (or a flat world with a flat sheet of a sun, or, or the sun being infinitely far away, outputting an infinite amount of energy, with the two infinite values being balanced, or ....).
A single pole means, in my view, that you're really only seeing half of the world (the DF logic behaves that way, although we're free to come up with any matching explanation we want. The DF world isn't even a spheroid...).
There are rather extreme temperature variations at the poles of the real world, although I think the range might be even larger in the Siberian interior. The differences around the equator are modest, and more a result of cloud and rain than the amount of light energy received (if the clouds were ignored).
The reason we have seasons on Earth is that its axis is tilted relative to the orbit around the sun. If the axis was at 90 degrees to the orbit, there would be no seasons, as the incoming solar radiation would be the same throughout the year, so you'd have a temperature gradient from the equator to the poles, but no variation over the year (apart from that caused by the orbit around the sun not being a circle, but rather elliptic, but the cycle of that doesn't match the rotation rate of the Earth around the sun, as the ellipse is rotating as well).