What is the temperature of intake air at several speed of sound intervals from 1x to 10x?
Thermodynamics is your friend here. Compression in a ram intake is ideally isentropic (meaning entropy stays constant, so the whole process is reversible). In reality, some viscous losses cannot be avoided but are in the low percentage range in a well designed intake.

The temperature $T$ in isentropic compression from a state 1 to a state 2 can be calculated from the pressure $p$ and the ratio of specific heats $\kappa$:
$$T_2 = T_1\cdot\left(\frac{p_2}{p_1}\right)^{\frac{\kappa-1}{\kappa}}$$

$\kappa$ is 1.4 for air, so if the saber engine flies in air 250 K cold (-23.15°C) and a pressure of 500 mbar, and the intake compresses this air by a factor of 10 to 5,000 mbar, the temperature will ideally rise to 483 K (210°C). In reality, this might well be 220°C or 230°C due to viscous heating of the air in the process.

How the temperature ratio depends on flight Mach number $Ma$ (again, ideally) can be seen from this plot, based on this way to calculate the pressure rise: