This is a huge grey area and my quest to find answers for them is never ending. I have referred to many performance books but to no avail. I hope this question can be clarified. Thanks
The engine is flat rated below Tref, and the thrust decreases above this temperature. The point of using a flex takeoff is to run the engine at a lower power setting, where its limit would be at a higher temperature. Using a temperature below Tref would result in the same thrust as Tref. The graph from Airbus below helps to illustrate the relationship between the variables.
Using a flex temperature lower than Tref does not make sense because it would not have any effect, I'll explain my point. The diagram shown before by fooot is pretty nice to see it so I'll refer to it.
After Tref we can see that the maximum thrust decreases, it is due to the temperature increasing and all the adverse effects that it usually have on an engine. However, below Tref we do not see the actual maximum thrust that the engine can produce, or else it would keep on changing in relation to the temperature. What we see is the maximum thrust the engine can produce without suffering structural damages.
I'll quote the Skybrary article about Flex temperature: "At low altitudes and cooler outside air temperatures (OAT), engine pressure is the limiting factor as the engine is capable of producing more pressure and, consequently, more thrust than the engine can contain."
Because of this structural limitation, the flight management system (FADEC in this case) will flat the rate at which the engine produces thrust until Tref. Therefore, the maximum thrust shown on the diagram after Tref is the actual maximum thrust, because the increase in temperature has decrease the perfomances so much that they are below the structural limitations.
In conclusion, selecting a flex temperature below Tref is the same as selecting TOGA, as it is in fact selecting the highest thrust the aircraft can safely produce.
I hope this helps and I hope it is correct!