The ISS - and other spacecraft - have several thermal regulation challenges. First, the ISS gets loads of direct sunlight for part of its orbit. Second, the other part of its orbit is spent in darkness but, in the universe's biggest Thermos bottle, passive cooling through even un-insulated space station walls would not be rapid. Third, regardless of the exterior heat input, the ISS has tens of kilowatts of equipment and human metabolisms dumping heat into the interior.
The standard practice for spacecraft (and space suit) designers is to take charge of exterior heat loads by loading up on insulation, slowing down the intrusion of exterior heat. Then, usually, you only need to worry about cooling rather than both heating and cooling. (This doesn't work perfectly; space suits have recently added hand and feet warmers for extended operation in shadow. But insulation is still a useful first step toward gaining control of spacecraft temperatures.) The reflective aluminum and white insulation on the hull of the ISS also helps resist exterior heat input. The layering of a reflective hull and insulation is a parasol of sorts.
You can add a further parasol to shade the hull, like the emergency measure used on Skylab, but ISS makes that difficult by stringing out its modules into a complicated jumble that also changes its angle with respect to the sun throughout orbit. (ISS can be stabilized with respect to the sun if need be.) You'd thus need a lot of parasols, unless you wanted one big one that would probably at least partly shade the solar panels. It's easier to add more insulation, though. Multi-layer vacuum insulation is fantastically effective stuff.
Once you're done with the parasols, though, you have the issue of internal heating. The ISS uses an average of (if I recall correctly) about 35kW at any time, with its solar arrays making up to 125kW available. NASA addressed that heat load by telling the astronauts to shut down a lot of electrical equipment (e.g., experiments), leaving the minimum on.
It couldn't really do much about the ~1kW per occupant, though, not without getting lawyers and astronauts rights activists involved.
Anyway, when you're buried under all that insulation and have seized control of heat loads, you still need a way to get the heat out. That's where the radiators and circulating ammonia come in, at least until a valve sticks. Most manned spacecraft have used a similar approach of insulation and radiators: the shuttle's bay doors were lined with radiators while the shuttle was wrapped in insulation. Capsules tended to use heat pipes and insulation, and heat control measures like the Apollo "barbecue roll."