Presumably it's so big that this amount adds up, and it's sufficiently isolated to heat up without losing too much power towards the outside

One square inch of your skin has a couple inches of flesh behind it making heat.

One square inch of sun has billions of inches of hydrogen behind it making heat.

Total power radiated by a black body per unit surface area scales as T^4 (in Kelvin).

So for black bodies with identical shape and linear dimensions R1 and R2, with identical power production per unit volume, both in thermal equilibrium with whatever is outside them, you would expect:

R1/R2 = (T1/T2)^4

(because setting power produced equal to power radiated gives R proportional to T^4).

Pretending humans are spheres with radius 1m and the sun is a sphere with radius 7*10^8m, you would expect the sun to have ~160 times the temperature of a human at equilibrium in vacuum. It's going to be lower because not all of the sun is power-producing, of course. But higher because a human is not 1m in radius. And again higher because humans are not spheres and lose heat more than a sphere would for the same volume (more surface area).

The sun is about 6000K on the surface. That would give us ~40K for the equilibrium temperature of a human in vacuum, which at least seems truthy.

TL;DR: the sun is big, with a small surface area compared to its volume, because it's big.