Lie on the beach in winter: the sun is pathetically un-warm.

Adjusting the angle at which you recline won't make the sun any warmer.

So your intuition is off here.

Imagine someone puts an opaque shell around the earth at cruising altitude, and cuts a metre-square window in it.

Put that window directly over the equator, wait for noon. You will have a metre-square patch of sunlight on the ground.

As the sun heads towards the horizon, the patch of sunlight stretches into a long east-west tail, just like a long shadow.

The same amount of energy is coming through the window, but it's spread over a much larger area on the surface, so there's fewer watts-per-square-cm hitting the ground.

Now move that window north 30 degrees. Wait until noon, and the patch is already smeared into a long tail north-south, and that's before applying any east-west smear. As the sun heads for the horizon, it's going to be even more spread out into a great big enormous oblong, extended in both directions.

Now, entirely replace that shell with windows, and through the raytracing gets more involved, the same principles are at work.

That's why mornings and evenings are cold, that's why winter is cold, that's why it gets colder towards the poles. You're getting a smaller and smaller share of the sunlight hitting the area where the earth is.