With some help from this thread, I've empirically derived most of the formulas governing heat transfers. These formulas are for one tick on slowest speed (rapidly unpause/pause). You can plug in the various values and determine what the temperatures will be after one tick. Hopefully this will dispel much of the misinformation regarding these things. If you discover something that does not follow these equations please let me know.
q is the heat transferred, divide by mass and SHC of the material to get it's new temperature. dT is the difference in temperature. k1 is the conductivity of the first material. k2 is the conductivity of the second material. klow is the lower conductivity of the two materials. kave is the average conductivity ((k1 + k2)/2). Conductivity of insulated tiles is not that which is display in the tile property box. It is the conductivity of the base material divided by 16,256 (ask Klei, not me). HC is the heat capacity of the hotter material (mass * SHC). Buildings have 1/5 the HC they "should" have, relevant when they are the hotter material or in determining new temperatures. Buildings include pipes, wires, generators, etc. but not built tiles.
Debris in a Tile: q = klow * dT * 200
Debris on a Tile: q = klow * dT * 12.5
Building to Tile: q = k1 * k2 * dT * HC / 10
Insulated Pipe to Contents: q = klow * dT * 10
Normal/Radiant Pipe to Contents: q = kave * dT * 10
Tile to Tile: q = klow * dT * 200. Further multiplied by 25 if gas with solid or by 625 if liquid with liquid. Another multiplier of 2 for thermium, 4 if thermium with thermium. There is clamping that can cause odd results, but this is the general rule. The change in temperature maxes at dT / 4 sometimes and dT / 8 other times for example. It's basically black magic.
Again, if you discover any edge cases do say so!