Why is space cold if the Sun is so hot?

Because "cold" and "hot" are describing two different things, and space has almost nothing to do the transferring.

Temperature is not the same as heat. Temperature measures the average kinetic energy of particles. Heat is the transfer of thermal energy. In space there are so few particles that the concept of temperature barely applies to the space itself — a very sparse gas can have a nominally enormous temperature while containing almost no energy in total, because there is nearly nothing there.

The three transfer mechanisms, and which ones work in space:

Conduction — energy passing through direct contact between particles. In a vacuum there is essentially nothing to conduct through. Absent.

Convection — bulk movement of a heated fluid. No fluid, so absent.

Radiation — electromagnetic waves, which need no medium. The only mechanism that works.

This is exactly why a vacuum flask works: the vacuum layer eliminates conduction and convection, and the silvered surface reflects radiation.

So what does an object in space experience? Only radiation, in and out. A surface in direct sunlight absorbs radiation and can become extremely hot; the same object's shaded side radiates away and becomes extremely cold. Spacecraft rotate — sometimes called the barbecue roll — precisely to even this out.

Losing heat in space is slow, which surprises people. With only radiation available, shedding heat is inefficient. The International Space Station's main thermal problem is getting rid of heat, not staying warm, which is why it carries large radiator panels.

The background temperature of deep space, far from any star, is about 2.7 kelvin — the cosmic microwave background, the residual radiation from the early universe. That is the floor.

What would happen to an unprotected human is not instant freezing. Vacuum exposure kills through lack of oxygen and pressure effects well before heat loss becomes the issue.