I'm glad you asked! So there's an important physics reason why the equator is warm and the North and South poles are cold on this planet, and it has to do with how you point a surface. If you ever find yourself in a dark office with a bright desk lamp (or maybe your home office or kid's bedroom might be suitable) you might even try this experiment: take a flat surface, a notepad or steno pad, and hold it up facing the light source, then slowly tilt it away and look at the color of the surface; you'll notice that it doesn't sharply transition from illuminated at 0 degrees to dark at 90 degrees -- instead it smoothly varies like the cosine of that angle.
This mathematical effect is incredibly important, it means that sunlight, during the day, averages out to being half as strong as its maximum over the whole of the Earth's surface. The calculation isn't even particularly difficult: the surface area of a sphere is well-known to be 4πr², half of that or 2πr² is illuminated at any one time, but the actual irradiation that we receive is proportional to the cross-section area, which is just the area of the circle: πr². So if the Sun-directly-overhead light were to be illuminating that entire half of the world, we would get k·2πr² light for some k, but instead we only get k·πr² light for that same k, so it works out to be 1/2 when averaged over the whole surface of the Earth.
While I was at university a fellow student asked me to guess the coldest place in the Solar System. I guessed "the middle of the dark side of Mercury." I guessed this for a couple reasons: (1) I knew I needed a rock without an atmosphere since atmospheres sustain convection currents that transmit energy, and (2) I figured since Mercury is so close to the Sun it's probably tidally locked to the Sun and therefore this part probably has not seen a speck of sunlight in millions of years.
It turns out that general relativity makes point #2 wrong and my friend gleefully informed me that he was looking at an article (there were many, so let's take [1] as representative) suggesting that it might be in a crater on the South pole of the Moon. This has basically the same reasoning of (1) and (2) above, except substituting the shadow of a crater for the shadow of tidal locking. But Mercury is still in the running -- the only issue is that we might not be looking at the dark side of it, but rather, again, at its poles.
[1] https://www.space.com/7311-moon-craters-coldest-place-solar-...