Imagine something like that happening in a slum. It's the combination of humidity, temperature and poverty that is deadly. Think mass casualties (millions of people). No air conditioned environments to escape the heat. Limited access to clean water. Flaky electricity systems that cause what little capacity there is to cool anything to fail. Temperatures at night drop a little but not by enough to provide much relief. Robinson does a great job of making you believe how real this would be and what it would look like.
The human body loses the ability to cool it self with 100% humidity. Sweat no longer evaporates. Basically, people start dropping like flies once that gets out of control. It's not survivable for more than a few hours. Any water you'd use for cooling no longer evaporates and would in any case have an ambient temperature that is close to or higher than your body temperature. Instead of cooling your body, it would just heat it up quicker.
This is a very near future science fiction novel that describes a very scary reality that we might be dealing with on a regular basis pretty soon. North West US and Canada actually got a sneak preview when temperatures in the US and Canada hit record highs last summer.