It turns out that getting rid of excess heat on the Apollo missions was one problem, but on the other hand various bits of equipment had to be kept warm to operate correctly.
First thing to realise: on the side of the Apollo spacecraft facing the sun, the temperature might be over 100 degrees Celcius, but on the side facing away from the sun the temperature was lower than -100 degrees.
The capsules were designed to eject heat efficiently into space on the non-sun side. They were also reflective, meaning that they would absorb less heat from the sun on the sunny side. The net effect, if the spacecraft cabin was not temperature controlled, would be that the cabin would become colder over time. To compensate when necessary, various heating mechanisms were built into the spacecraft.
During the Apollo 13 accident, when a lot of non-vital systems were shut down to conserve power, there was insufficient heating to prevent the cabin from cooling passively, as it was designed to do. That's why the astronauts became cold.
Apparently, despite the astronauts feeling cold, nobody at NASA was particularly worried about the crew health being seriously threatened by the cold. The astronauts weren't comfortable, but nor were they in immediate danger from the cold.
Another plank in the moon conspiracy theory is broken. Probably Fat Freddy already knew about this debunking. If not, now he knows.