What do you need?:

(1) To calculate the thermal resistance of the case theoretically using phisics and math.

(2) To determine it experimentally.

If the answer is (2):
a) Determine the average heat generated inside the case (electrical power).
b) Measure the temperatures inside and outside the case (as Steve said), after some minutes of operation.

Apply the formula.

Of course, the thermal resistance depends on the existance of air flow outside the case and also on the case environment: Air gaps between the case and other elements, etc.

Alfredo.