How much aerodynamic heating do jetliners endure?
Based on the formula already shown in this answer, we can calculate the TAT (true air temperature), which is the temperature reached at the stagnation point1, from the SAT (static air temperature) and Mach number:
$$ \frac{\text{TAT}}{\text{SAT}} = 1 + \frac{\gamma - 1}{2} M^2 = 1 + \frac{1}{5} M^2 $$
The resulting plot of TAT vs. Mach number at the SAT of -56.5°C (ISA tropopause) is shown below:

As you can see, a subsonic airliner (I assumed Mach 0.85) will still experience temperatures below freezing. Concorde however was reaching temperatures of around 120°C at cruise speed of Mach 2.02. This was already close to the limit:

Maximum Total Temperature (TMO):  127 Degrees Celsius (on nose)

(Concorde Performance)

As requested in the comments, here is a larger speed range including the SR-71:

The temperature could reach almost 400°C at Mach 3.2 (What is the true top speed of the SR-71?), but note that the SR-71 used fuel to cool the skin (the windscreen was the hottest part at 316°C according to Wikipedia.

1The TAT is measured by the aircraft with a probe that brings the air to rest w.r.t. to the aircraft (stagnation). The kinetic energy of the air is therefore converted into thermal energy, raising the temperature. The surface temperature of the aircraft at points where no stagnation occurs will be at a lower temperature. Thanks to Peter Kämpf for pointing this out.