You are pretty much correct. Except that you may still be slightly confused on step 2.
Once the thermal properties are known, the egality of is computed and then stored. This means equation the linear and log laws, and solving for the value of at which they intersect. Note that this special intersection is then called . This value is only computed once. The thermal wall functions only needs the value, but it needs a way of determining which law to use. During the computation, the local is compared to the precalculated value to determine which law to use. The thermal wall functions are identical to the velocity wall functions. However, for the velocity functions we know beforehand the intersection of the linear and log regions since these are independent of fluid properties. The thermal law of the wall instead can only be computed after all thermal boundary conditions have been applied. 
You meant .
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About step 2, I'm still under the impression that in order to find where the 2 profiles intersect, a clever way is to equate their equations. What am I missing? Fluent equates the profiles and performs some iteration process (like narrowing the right value starting with a low and high value...)? 
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Correct, computed only once. In other words, it is not recomputed on subsequent iterations. This computation is probably done during the initialization step. You must equate the equations,that is the only way to do it, I would not describe that as a clever equating. I imagine Fluent calculates it by some iterative process like you described, but ignoring the details of how it is calculated, it is a simple find the intersection of two curves problem. Pretty much any algorithm will work. Bisection works. Fixedpoint iteration and NewtonRaphson are also guaranteed to work since one of the equation is a line, and that would converge very quickly (Richardson extrapolation can be used to speed up convergence also). I am sure that Fluent has these algorithms prepackaged in the background somewhere since they are also needed when solving the large systems of equations during the iteration process. 
All right, thanks for the clarifications. Case closed.

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