Space is hot because the average kinetic energy of particles is very high. Space feels cold because there are very few particles in a vacuum. It's like a tiny spark from machinery being very hot individually, but because the spark is so small, it doesn't do much energy to your body.

how a capsule with three people inside is able to freeze when the exterior is exposed to direct sunlight.

The core of the question is: What defines the temperature of the capsule?

While it's intuitively clear that the astronauts (~3×100 W) and electric devices (if they are running) generate heat in the interior of the capsule, on the outside it's more complicated:
The first thing that comes in mind is the sun shining onto the capsule (even throug a sphere defined by the solar orbit of the earth with the enormous power of 1361 W/m^2 ) heating up its surface. Yet, as the surface of the capsule is made of shiny aluminium, only 20 % of the radiation is absorbed, the rest is reflected. Additionally, the radiation effectively acts only on an area defined by the cross section of the capsule, not the entire (semi-spheric) part of the surface directed towards the sun. But anyways, the surface subjected to the solar radiation heats up and...
... itself emits heat radiation into space with a power proportional to the 4th power of its absolute temperature (~ T ^4 ). The remaining heat from that source is conducted along the hull of the capsule and towards its inside until an equilibrium temperature distribution is reached, where the heat generated by the astronauts (and devices), the heat intake from the sun, and the negative contribution due to heat radiation on the entire surface are in an equilibrium state.
The NASA engineers surely have designed the properties of the capsule in that manner, that a comfortable ambient temperature inside the capsule is preserved when all electric devices are running as planned (i.e. the comfortable temperature is the equilibrium temperature in that case).
As in the emergency situation, these devices were turned off, the equilibrium temperature which adjusts by itself is significantly lower than the designed comfortable temperature.

I guess that because the interior isn't a vacuum, the slow-moving air molecules were able to dissipate heat.