As in sympathy, Alar is required to shape the conduit that changes or moves energy as part of sympathy or sygaldry. However, that conduit itself does not require energy, beyond the effort of the maker to create it.
Your example of Anker's fridge is flawed. The only law that sympathy and sygaldry respects is that the energy has to come from somewhere, that it cannot be created or destroyed. Making energy move in unnatural ways is the entire point. In the fridge's case, moving energy away from where you want it to be cold. The metal strips that are runed take the heat (even though there's very little) from the inside and move it to the outside. Energy is preserved, because it will get hotter outside the fridge. The heat exchange itself is created by the Alar, bound into permanence using the runes, and worked simply until damaged.
When sympathists are concerned about their own body heat, it's not the binding itself that draws or adds heat. It's using their own heat to accomplish something on the other end of the binding that causes chills. In the famous case of the classroom duel, they have to light a candle, without heat from anywhere else, thus the chills to their body. In the case of cooking themselves, it's slippage when there is another heat source (say, lighting a candle using a bonfire, or deliberately taking a building on fire and moving the heat away to put it out like Kilvin and Kvothe did), and their Alar or conduit isn't perfect enough. Energy can't be created or destroyed, so when it doesn't all go where the sympathist wants, it ends up dumping at least partly into the sympathist.
Remember Kvothe's example of the coins early on. He created the link between two coins, but that did nothing to the coin and nothing to him. Only when he moved one, and thus moved both, did the link take energy, and it took it from the momentum of the coin he moved, which was appropriately twice as heavy.