As the myth goes, drinking cold water after meals will cause the oils and fats that you have just consumed to become solid. This "sludge" is supposed to react with the acid in your digestive system, line the intestines, turn into fat, and cause cancer.
This myth is busted on several accounts, starting with the entire premise that drinking cold water will turn oil into solid sludge. Our internal body temperature is a steamy 98.1 degrees, and it typically takes 2 to 3 hours for a meal to empty from the stomach and move into the small intestines. This is plenty of time for all of the liquids and solids in your stomach to become the same warm temperature. Additionally, during these 2 to 3 hours of digestion, the stomach mixes and churns it contents until everything is a similar consistency. Once in the small intestines, food is broken down further into carbohydrates, protein, and fats and absorbed through the wall of the intestine and into the blood stream. Fat does not remain in the intestine for an extended period of time.
While it is true that an accumulation of a large amount of body fat can put you at a higher risk for certain types of cancers, this has nothing to do with the temperature of the water you drink before, after, or during meals.