How would society adjust if Fire was reserved for the elite? What would society do in order to survive?
The following presumes next to no magic and only the beginnings of modern technology, which is really limited if there isn't fire to meld and shape metal. Metal, glass, sterilization, lighting, lighter than air travel, steam, and the beginnings of electricity will be greatly limited.
The following jobs may become religiously indoctrinated to counteract the near crippling effect this would have on civilization: Blacksmiths, Glassblowers, Doctors, Dyemakers, Pilots/conductors, Engineers, and if they would be around, Electricians.
Alternate forms of heat would have to be distributed to groups or settlements of humans and other mammalian life forms. These settlement structures would have to either hold in natural body heat, be controlled by a single "fire elite" that produces fire for his charges, or produce heat by some other means, like electricity and heating coils or being built over natural year-round hot springs. --This single fire producer to multiple subjects smacks highly of a feudal rule system where fire is the payment instead of gold.
Desirable housing would become much more slender, but with thicker walls, as natural light may not reach into the far reaches of structures like castles and keeps. The most defensible non-fire based buildings would be free standing stone towers built around a single staircase. The majority of room separating items in any building would have to be held together with wood. Just imagine medieval castles with shoji screens! If it's too costly to create buildings with metal, the majority of structures will revert to stone, wood, straw, mud-huts and caves. This means many buildings will be single level, or double level if made of stone and shaped lumber. There may also be a surge in tree-houses as they provide protection from most land-based predators.
Reading and writing may become less prevalent, as time (and thusly natural light) is removed from the standard workday OR beings may wake up before dawn more often to counter not being able to do much at night. Which means scholars may be taking manpower away from any farming town by virtue of spending their daylight hours reading and doing mental exercises as opposed to working fields. This means scholars may not exist in areas heavy in farming and/or have moved into more urban areas where less time is needed to maintain grounds and produce a product for consumption.
Personal vanity may take a dive as there will be less glass and metal for crafting mirrors; however, the processes to make cosmetics may still be around. The public at large may be less attractive, but the elite will still have the opportunity to use dyes and coloration to enhance their appearance (Some cosmetics need to be boiled to create them, similarly some dyes need to be drained from their various sources which can be accomplished by a cooking-like process).
I imagine that there would be large areas that cook meals for the surrounding populous IF the 'fire elite' form a centralized government-like network. They reach out to the people, but predominantly, the people must come to them to receive the 'blessings of fire'. As a point of flavor if cooking is relegated to the elite, so will seasonings. (Which means that fire-controllers may enjoy spicy food! How's that for flavor?) The population at large will have a diet that consists more of fruits and vegetables that do not need to be cooked to be consumed. (They may be more fit than usual?) Bread, a baked good, will be rarer. Cakes, rolls, doughnuts, tarts, and the like will be aimed more towards the elite due to the restriction. Even porridge, unless it is distributed by the ‘elite’, may be a delicacy the majority of people have yet to even hear of. With this high concentration of carbohydrates in the diet of the Elites a great many of them may be overweight.
With the removal of fire from public use, sterilization may also become a thing of the past, available only to the elite. Without boiling water and fire to sterilize tools for surgery pregnancy, mauled limbs, and broken bones are much more risky to treat. If only 10 people out of 30 can create “hot water” when a pregnant woman goes into labor, how will we enjoy that self-same western movie trope where someone calls out for hot water? I'd imagine there would be a lot of shrugging and panicking.
Fireflies and other light producing animals, insects, and invertebrates would become a luxury pet and valuable commodity item to provide light to those who could afford them. Glowing fungus with eldritch light would become something you no longer see solely in caves if someone can figure out how to transplant them from cave walls to wooden and stone structures.
Finally, clothing would become heavier for nighttime use. During cold winters with limited heat, body heat would need to be used to maintain core temperatures. This means more furs and heavy clothing during the winter months, which in turn means more dead animals and more focus on textiles, taxedermy, and leatherworking to reduce waste.
With the introduction of heat and light producing magic, provided it is widely available enough, there would be no dramatic change to the way life is presented. Only the methods of creating that light or heat would change, and may be relegated to flavor instead of focus. At most, in a DnD4e setting, anyone with rituals that produce heat and light may become the new 'power companies', providing their specialties for fees and services.
Society as a whole will most likely shift its hours of activity to work in natural light. Life would become more outdoors based. Science and magic would be visually and temperature focused. If the Fire was removed suddenly society would not adjust well. If fire was slowly removed, the transition would barely be noticed until it was too late.
Naturally produced fire would be hoarded. Anyone with the ability to produce fire through normal methods (rubbing sticks together, etc) would become either instantly reverred or feared by the public and a target of the 'hot-headed' elites.
The preceeding argument assumes that the civilization is restricted from movement, otherwise all the cold people would just move somewhere warmer and re-establish settlements.
In summary: Life sucks for them. They wear more blankets and build different houses and die alot, unless they move to somewhere warm.