The space between the Sun and the Earth *isn’t* cold because it isn’t *any* temperature at all. Space is nothing, and nothing can’t have a temperature. Stuff *in* space has a temperature. Anything i*n* space between the Sun and the Earth will actually be very hot unless it’s something is in between it and the Sun, in which case it will be very cold.
When we say space is cold, it’s kind of misleading because what we’re really taking about is the temperature of the very sparse bits of gas and dust in a given volume of space. Since there are so few molecules or bits of gas and dust in any given volume of space, it will have a low temperate, just like how it’s cold at the altitude planes fly at because the air is so thin.
Stuff *in* space can get very hot though. The sun-facing side of Mercury gets as hot as 800°F (430°C) while the side facing away from the Sun gets as cold as -290°F (-180°C). Earth is farther away from the Sun so it gets less concentrated energy, which means it doesn’t get as hot. Using the Moon as an example (since like Mercury, it has no atmosphere), the sunlit side of the Moon gets up to 250°F (121°C) in daylight and as cold as -208°F (-133°C) on the dark side.
So in summary, your instinct is mostly correct. Things *in* space are hotter the closer they are to the sun, unless something is blocking the sunlight, in which case they get very cold.
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