I think it is quite counter-intuitive that some lenses or mirrors focusing sunlight to a single spot cannot produce a temperature higher than Sun's Surface.
It is indeed counter-intuitive because it is not possible to focus sunlight to a single spot.
As a simplification, let us consider the sun to be a perfect black body. Then if we know its surface temperature (5772K according to wikipedia), we can calculate its heat flux (63000kW/m2) according to the stefan boltzmann equation. If we know its thermal power output, we can then derive its diameter (which is quite a bit more than zero.)
The sun is not seen in the sky as a single point. From Earth, it appears to have a diameter of about 0.5 degrees (that is to say, if you point a telescope at one side of the sun, you have to turn it through 0.5 degrees to point to the other side.) This angular diameter of 0.5 degrees (or about 1/100 of a radian)is a function of Earth's distance from the sun, and the sun's diameter, which is related to its heat flux as described above.
Imagine I have a parabolic dish reflector on Earth that is perfectly manufactured. With this I can concentrate the sun's rays about 10000 times (no more, because of the 0.5 degree angular diameter of the sun.) I will not give a geometric proof here but if you use a ray tracing program you will find that a parabolic trough can concentrate a light source of 0.5 degree angular diameter about 100 times, and a parabolic dish will be the square of that.
The normal radiant flux on Earth is about 1kW/m2, so I can get about 10000kW/m2 heat flux and a temperature of about 3644K.
As you can see, this is comparable to but slightly lower than the temperature of the sun.
To get higher temperatures from our solar concentrator we would need the sun to maintain its output but be smaller to give us a better focus, but then of course the sun would have a higher surface heat flux and surface temperature!
What could a scientist deduce from that peculiar behaviour? Any quantic property in example? Or something about optics?.
As explained above, the behaviour is not peculiar. What can be deduced about optics is that an optical system cannot produce an infinitesimally small point focus from a spherical black body light source of finite diameter. This conclusion can also be derived geometrically.
If it were possible for a temperature source to raise the temperature of another body above its own temperature in a closed system, there would be interesting consequences for the validity of the zeroth and 2nd laws of thermodynamics.