The short answer is that the overall average temperature of Neptune is the coldest, and the average temperature of Uranus is the coldest recorded.
The long answer is that the answer to this question used to be simple. Pluto is the planet furthest from the Sun and the coldest planet. However, Pluto was no longer classified as a planet in 2006 and is now known as a dwarf planet. So, which is the coldest planet in the solar system right now?

True-color photograph of Pluto taken by New Horizons, july 2015.
This sounds like a simple question, but in reality, there are two planets that fit this title. It all depends on whether we're talking about the average temperature of the planet or the minimum temperature that the planet reaches.
Most people would say that the coldest planet in the solar system is the coldest neptune. This is because he is the eighth planet in the solar system, which means that it is the farthest away from the sun. The sun is our main source of heat, so it makes sense that the planet furthest away from it will be the coldest. Neptune is called the Ice Giant, and for good reason.
This photo of Neptune is the last photo taken by green and orange filters on the Voyager 2 narrow-angle camera. The image was taken in August 1989, about 4.4 million miles from the planet.
Its average temperature is around -214 degrees Celsius. This is much colder than Earth's average temperature of 15 degrees Celsius. Neptune lacks a solid surface itself, but instead has an icy layer of water that acts as the mantle of the planet. This made it difficult to find surface temperatures, but studies from missions conducted on Earth and flight successfully extracted this average temperature from the upper atmosphere.
The cloud bands in the upper reaches of Neptune form shadows at the lower clouds.
Curiously, though, Neptune holds the title of the lowest average temperature, it is the seventh planet from the Sun, and Uranus has the lowest temperature recorded. This record reached a very low -224 degrees Celsius.
Voyager 2 photographed Uranus in 1986
This was unexpected, as Uranus is 1 billion miles closer to the Sun than Neptune. That's a long way! So how can it be colder? Well, despite the great distance between these two ice giants, they are both far from the solar system, and the sun has little effect on the temperature of the planet. Any heat is mostly caused by the motion of the planet and its interior, and the differences between those motions and interiors are there.
The Hubble Space Telescope's image of Uranus can see cloud bands, rings, and some moons.
There is a theory related to the strange position of Uranus. Uranus is on a 98-degree axis, which means that the planet is rolling around the Sun on one side of it. This is unique, and although some planets are slightly inclined, none of the other seven planets in our solar system do.
Comparison of the sizes of Earth and Uranus.
Astronomers aren't entirely sure why this is, but it's thought that long ago when the solar system first formed, Uranus was hit by a large object. This object would have to be very large, maybe even as big as Earth, to knock the entire planet off its axis. This will cause huge disturbances to the Earth's core, and in the process, due to its strange orientation, heat continues to spill out of the Earth's atmosphere, losing a lot of heat.
The near-natural color (left) and the southern hemisphere of Uranus at long wavelengths (right) show the faint cloud bands and crowns seen by Voyager 2 in the atmosphere.
Both Neptune and Uranus have very similar atmospheres, both containing high amounts of methane. Methane is a gas that traps heat very well. It will try and retain heat to reach the planet. Neptune has slightly higher levels of methane in its atmosphere and is therefore more efficient at maintaining the heat generated by its core. As a result, Neptune has more heat in the first place, and the atmosphere retains heat better.
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