I don't think the food raises their temperature, though I'm no expert in this either. Warm blooded animals use a portion of our metabolism to maintain body temperature (endothermic) while cold blooded animals (exothermic) have to get most of their heat from outside sources. This is why they bask in the sun and look so happy.

They need heat the same reason we do, to allow our bodily functions to operate as our organs expect them to. Things like metabolism slow or cease when required temps can't be maintained.

When I was on the airboat gator tour in Florida, the guy was saying the gators sort of ferment their food to help break it down, so they need that heat (73F, I just googled) as a minimum to actually digest. He said otherwise food can end up rotting in the stomach and they can get sepsis and die.

While we have to eat and metabolize more to maintain our core temp, but that lets us go into hotter or cooler climates and have a chance to keep surviving as long as our bodies can balance out our temp by burning calories and sweating.

Other than lower required caloric intake, I can't think of any advantages of being cold blooded.