If the Sun is able to keep Earth warm while being millions of miles away, shouldn’t it get warmer and warmer the closer you get to it (like when you go to space)? Like how it would get warmer if you were to approach a burning house for example?
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The short answer is that that space is hot, but before getting there we have to be careful when talking about the temperature of space.
The temperature of an object is straightforward enough to describe. We look at the kinetic energy stored in the object at the molecular level, recognizing that that’s the quantity that will come into equilibrium if two objects are placed in contact with each other and allowed to transfer heat between one another.
That definition falls on its face when we start looking at the temperature of nearly empty space–no vacuum is perfect. If it were perfect vacuum then there would be no matter to have kinetic energy, thus rendering the notion of average kinetic energy meaningless. However, since there are a few particles here and there we could take their average kinetic energy and come up with a temperature. That temperature has no real relationship with what temperature an object would be heated to if left in that position, though. For example, the ISS orbits in Earth’s thermosphere which is nearly a vacuum, but the remaining gas particles at that altitude have a temperature of up to 4,500 degrees F. That’s plenty to melt most materials, but it poses no risk to the ISS because there’s not enough gas there to actually transmit meaningful amounts of heat.
That gives rise to a better definition of temperature in space: if you were to put a thermometer out there, what temperature would it be heated to? Since heating via conduction (touching) and convection (moving fluids) are negligible this just leaves heating through thermal radiation. In deep space there’s basically no heating from any direction except the sun, but that heating is substantial. If you put a thermometer in direct sunlight in space then it would be heated to be rather warm–it’s basically being left out on a summer day at permanent high noon in a tropical climate, but also with no heat being blocked by the atmosphere and no heat being moved around by air or water.
The problem with this definition is that it’s highly dependent on the shape and color of the thermometer in question. If the thermometer was long and skinny and oriented just a tiny end towards the sun then it would shed lots of heat along its length and report a lower temperature. Make it more like a disc and orient the flat surface towards the sun and it would be more effective at catching the sun’s light. Paint it to be shiny and it’ll reflect most of the sun’s energy, but paint it black and it absorbs a lot of energy.
That’s how there are so many different temperatures that can be used to describe space. For example, the James Webb Space Telescope makes use of a multi-layer sun shield that is designed to reflect the sun’s energy away from the telescope. That leaves the cold side only subjected to the radiation from deep space, which is just a few Kelvin. The ISS takes a more moderate approach, but it has large radiator fins on one side (they look like solar panels, but they’re white and oriented 90 degrees off from the panels). These have most of their surface area oriented towards deep space to shed heat in that direction, while parts of the ISS are bathed in sunlight and heated to fairly high temperatures (a couple hundred F on the high end).
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