I heard on Doctor Oz once that drinking cold water can help burn calories in a rather passive way since the body will have to work to warm it back up. Would this concept work practically in general? Could I just turn down the thermostat some, and it help me lose weight?
@svrist is right in his comment. However, in nutrition, 1kcal = 1 Cal. So, if you drank 1 gallon of freezing cold water, you would burn about 140 calories. Besides being extremely difficult, this isn't really significant enough to make a big difference. But if you're staying hydrated at the gym, you might as well do it with ice water to squeeze out an extra few calories. However, if you're looking to lose weight, remember your body will retain a lot of this excess water causing you to gain weight (although healthy weight). As far as turning down the thermostat, it might save on your heating, but you'd be lucky to see any difference without turning the AC on overdrive (simply, just no).
Honestly, there's almost no way this can be true. This question was answered on Straight Dope.com (though there they tried using beer...):
It takes 36.000 calories to heat one liter water from 0 to 37 degrees Celsius. However, the calories we use in food energy are kilocalories, so that's only 36 kcal.
Assuming you probably only drink 2 liters tops, that's a whopping 70 kcal you just burned there!
However, this is drinking nearly freezing water, which is highly unpleasant. And because the water travels through your body, the heat loss is spread out through your mouth, gullet and stomach. This might not reduce the local temperature enough to get your body actively warming it and potentially could be warmed up from your regular activities, so there wouldn't be a net gain.
A more positive side effect would be that drinking lots of water fills your stomach and might reduce your need to eat, which probably will do more for your diet than the actual body warming.