Well, I could always design the enchantment as a small (movable) doorway. That would give me access to the bonuses "+5 magical transportation" at a minimum, or perhaps even the "+7 bonus to affect movement through" (the heat moving through the doorway is projected farther away into the room).
And it's even appropriate to the concept of the magus, who has a minor magical focus in portals. Would it apply?
Keep in mind that Rego does not create heat, which means you may have difficulties justifying how you are achieving that "no extra expenditures" provided by Magical Heating even when used to simulate "excessive heating". However! I think it would be perfectly reasonable to say that Rego Ignem is making some parts of the lab really hot while keeping others really cold. You'd even get refrigeration "for free"!
As stated above, if you chose this, I would not allow you the benefit of cost savings that Magical heating allows -- but if you had some other means to have free or almost free fuel (one would simply be a CrIg Ring duration spell) it would not be an issue. This could also be solved by adding an extra magnitude for slightly unnatural control (Base 4) -- so that you could make some areas really hot by making others really cold (see above).
I disagree -- if you are controlling at "long range" either you must give it range longer than Touch, or range larger than Individual (probably Room, though if your lab is circular, maybe you could enchant the item as one large Circle?)
So I would make it:
ReIg 30: Base4, +1 Touch, +2 Room, +1Conc, +1flexible heating (you can readjust heating as you like) +5 levels Item maintains concentration.
You could drop it by 10 points if your lab is circular and you enchant a large ring (possibly of some durable material -- but a tapestry of dancing fires would be colourful and appropriate) surrounding it. You could also drop it by 5 points and take the Base down to 3, sacrificing the ability to make some areas colder and only redistributing heat from some source you already have (this would not allow you fuel savings, however)!
Well, keep in mind that regular heating was usually provided by a fireplace and that in period those fireplaces were very inefficient -- most of the heat produced by the fire was immediately sucked out through the chimney. Heating was provided indirectly by the stone heating up and radiating into the room at short distances.
So the Rego Ignem effect would capture the heat touching the item (which is close to the fire) and move it into the room before it gets sucked out through the chimney.
My reasoning is that increasing the efficiency of the fireplace means that it provides the lab with more heat by using the same fuel.
More heat kept in the lab = Superior Heating or Excessive Heating. Doing it through magical means = Magical Heating.
Refrigeration is not the goal here, and not even beneficial, as the lab is in the basement. It will already be cool by default, which is why I'm looking at improving heating through magical means.
Well, I can agree that moving the heat farther away might warrant an additional magnitude, but not with the rest. My objective here is to make an item that can easily be enchanted as a lesser item.
I think taking the teleportation guidelines are more appropriate. The spell Invisible Hand of the Thief (MoH p.93) presents a guideline for transporting something away, with +1 magnitude for up to 50 paces. I think that's a more appropriate here: the item is not reaching out from afar to pull the heat away and move it elsewhere, it's projecting the heat it receives farther away instead of allowing it to be pulled out through the chimney.
That does not save fuel directly, but it means that the fuel you would have used anyway is much more efficient. That means more heat remains in the room. Better heating at the same cost = Magical Heating.
Base 3, +1 Touch, +2 Sun, +1 project heat up to 50 paces away; +4 levels for constant use. Total level 19. You adjust the heating by changing the distance between the item and the source of heat.
ReIg 20 Tame the Laboratory Fires R: Touch, D: Sun, T: Room
This spell keeps all the fires and flames in the Target room calmly and safely in their respective fireplaces, on their wicks, etc. They don't jump around no matter what happens in the room, and stay where they are supposed to burn. The heat they generate is evenly distributed over the entire room.
(Base 3, +1 Touch, +2 Sun, +2 Room)
This spell can be made into the constant effect of a lesser enchanted device of level 24. Only one such item is needed to safeguard a lab. Controlling the lab's heating is done entirely by controlling the fires in the lab - so who did it before can do it still now, with the device around.
Applicable Shape and Material Bonuses I came up with are: Ruby (+6), Wand/Staff (+4), Basalt (+3), Hickory (+4), Ring (+2), Fired Clay (+4). How's a wand from hickory or basalt, then, hanging from the ceiling of the lab?