Can a timing belt cause the car to overheat?

Yup, if it's loose and it's run by the timing belt. You didn't list an engine size so that's a generalization but it applies to any engine with a water pump that is one of the idler pulleys.

Although the timing belt does operate the water pump, if the belt slips in any way the engine will cease running which makes it a moot point. It can't cause overheating unless it's just a water pump leak that doesn't effect the timing belt so to answer your question, no, a timing belt cannot cause overheating.

Happened to my 3.0L Grand Voyager with a freshly rebuilt engine. The tensioner pulley is spring-loaded to set the tension, then a nut is tightened to hold it there. The students didn't realize the bracket was sticking and not pulling on the belt. I made it 40 miles on a mid-summer day before it started to run hot. Found out we could turn the water pump pulley by hand, but the belt never jumped a tooth. While playing with that tensioner, we found we could duplicate its sticking consistently. A simple nudge with a small pry bar solved the overheating.

Now, to be fair, this belt was just installed, and it was tightened improperly. You're right that if a correctly-tensioned belt becomes loose thousands of miles later, it is likely due to other more serious problems, but the point is it can happen. I had a water pump go out on my daily driver, another 3.0L Grand Caravan. It made noise for two months to give me plenty of warning, .. So I ignored it as long as possible. It finally started overheating when all the water fell out as fast as I could pour it in. I'm not suggesting anyone else ignore what might be a timing belt issue. The 3.0L is a non-interference engine so the worst damage would be to my pride as I was walking home. Most newer small engines ARE of the interference design, and a simple timing belt problem can go from somewhat involved to real serious and expensive if it breaks or jumps more than a couple of teeth.

We don't know the engine size, what the symptoms are, or any other details, so normally a sudden overheating concern with no other symptoms is not likely to be due to the timing belt, but can it happen? Yes.

In this particular case, neither engine available for this vehicle has a water pump that is driven by the timing belt. They are both driven by external serp belts so in this case it is impossible.

Dandy point, but as is becoming WAY too common, people don't bother listing the engine size when asking engine-related questions. I found nine engine sizes for this year and model with a total of 13 gas gas or diesel variations. To add to the confusion, some show a timing belt-driven water pump AND a non-timing belt pump for the same engine size. You have to either know the engine code or simply go by what you see on the engine. In this case we don't know anything other than the year. This severe lack of information, details, clues and observations, even symptoms, is getting frustrating.

This model only has 2 US engine options and one of those is diesel.

http://www.rockauto.com/catalog/x,make,VOLKSWAGEN,year,1999,model,GOLF,vtype,US

Just because they're listed here doesn't mean they sold them in the U.S. or sold very many. This is all I have to go on. I avoid Volkswagens whenever possible, ever since I worked on one in the late '80s with a single adjustable tie rod for setting total toe. They were too cheap to make the other side adjustable. The crumbling cardboard panel under the glove box was another impressive point. To me, "German engineering isn't better; it's just different.

Those catalogs are generally inaccurate. Alldata will list all options that are actually available in that specific model and year. And they only show 2.