Integral Boundary Condition - Problem

For the sake of simplicity, I'll use an example of stationary heat transfer in a 2D geometry.

My goal was to create a boundary condition such that the total flow of a boundary in the z-direction had a value of 1, yet its local flux could be non-uniform. Furthermore, at the same boundary, the temperature distribution was at a single (but unspecified) uniform value. From reading these forums, this was my approach:

1. Create a constant temperature boundary condition at an undefined variable "T0"
2. Create a local integration model coupling along that boundary: "IntegBottom()"
3. Define a Global Equation: IntegBottom(-Tz)-1=0, where I define T0 as the state variable
4. Make sure the solver is using both the Heat Transfer model and Global Equation

When I check the Derived Value of a Line Integration of -Tz along the same surface, I get a value of - 0.353 instead of 1. I'm not rotating the integrals or taking the surface integrals. The solution is dependent on the Global Equation, yet I seem to be misinterpreting Step #3.

Any ideas what I'm doing wrong? Thanks.