Why do we see a reduction in temperature in a wind tunnel by increasing the velocity, but in a real flight it's the opposite?
I believe the reason is that the air is cooled while compressed in the high pressure reservoir before the high speed wind tunnel.

When moving air is stopped (as happens around the leading edges of the aircraft), its pressure increases (per Bernoulli's principle) and since the compression is adiabatic (no heat exchanged (yet)), its temperature also increases. The final temperature is called Total Air Temperature (or stagnation temperature).

For flying aircraft, the total air temperature is its original temperature plus the increase due to compression by the leading edges of the aircraft. That's why the leading edges heat up in supersonic flight. The other sides don't, the air is not stagnant around them.

However, for wind tunnel, the air was already stagnant in the high pressure reservoir before it—high-speed wind tunnels usually pre-compress the air, because compressors can't produce supersonic speeds. It this reservoir it cools down, and then as it accelerates down the wind tunnel, it adiabatically expands, reducing its temperature well below ambient. It returns to the temperature in the reservoir at the leading edges, but around the rest of the model the air is not stagnant, so it has the lower temperature of the flow.