Why did the orbiting Salyut 7 get so cold when its electrical systems malfunctioned and its batteries drained empty?

A spacecraft's thermal control system is designed to handle normal heat loads, balancing heat generated by electrical systems inside (and humans in the case of crewed vehicles) with heat loss through the skin and heat gain from the sun. While I'm not familiar with the specifics of the Salyut 7 case you cited, if they lost electrical power then all of the heat generated by the onboard systems stopped while the heat loss continued. As the vehicle began to cool, electric heaters probably turned on to protect the propulsion lines from freezing. In short order, the batteries were drained (especially if the vehicle's attitude control system was also offline, meaning the solar arrays weren't correctly pointed towards the sun). This is very similar to the situation on Apollo 13. When they turned off so many electrical systems, the heat loss through the vehicle's skin was greater than the heat generated by body heat and heat gain from the sun. As a result, it got really cold inside.

I used to control DSCS-III military communications satellites. The thermal control subsystem consisted of passive and active devices to maintain the proper operating temperature. The passive methods included reflective mylar coatings, insulation, and optical solar reflectors (similar to mirrors) mounted on parts of the satellite. Being a communications satellite, there were a lot of heat generating components on the inside. There were also thermostatically controlled heaters on critical components like the propellant lines. If the satellite lost Earth-lock, it went into survival mode. This caused it to load shed as much as possible. The communications system, attitude control system*, and many other electrical loads were turned off. As a result, the heat produced inside the satellite was much less than normal and the internal temperatures would start dropping fast. As they did, the thermostats would turn on heaters increasing electrical consumption. If that happened, the batteries would be dead in about 6 hours and the satellite would be lost. Our quick recovery plan was to attempt to put the satellite into sun-hold mode (solar arrays pointed at the sun without regard to Earth pointing attitude). Once you had it in sun-hold mode, your batteries could recharge and you had much more time to regain control of the satellite. Whether you'd ever get all of the components to turn back on or not was a crap shoot. Some of the old tube-type travelling wave tube amplifiers (TWTAs) didn't take well to being turned off.

*If you lost Earth lock, it was assumed that the attitude control system was malfunctioning. Therefore, there was no need to keep it on wasting electricity.