Clutch should lock up when the "clutch" is hot, not necessarily when the "car" is hot, but there is often a relationship between the two. Heat is transferred to the clutch via conduction (through contact with the engine assembly through mating surfaces and bolts) and convection (from air flow or lack thereof through the radiator).
For example if the engine is warmed up, the clutch could lock up while sitting at a traffic light in hot conditions, then as you get air flow when driving it could cool the clutch enough to cause it to release. If there is enough air flow through the radiator do that, the fan is not necessary. A clutch release saves energy. The fan spinning a bit after the clutch releases or engine is turned off is normal, an indication that it is not seized in a locked up position.
I have not done it but would think that a bench test with a heat gun might be a decent test. Of course without specified temperature setpoints and measurement points that is still a subjective test. I think I'll do that soon, and I'll include thermography data as part of the test.
