We present mid-infrared ( 8 – 33 μ m ) observations of the binary L5-Trojan system (617) Patroclus–Menoetius before, during, and after two shadowing events, using the Infrared Spectrograph (IRS) on board the Spitzer Space Telescope. For the first time, we effectively observe changes in asteroid surface temperature in real time, allowing the thermal inertia to be determined very directly. A new detailed binary thermophysical model is presented which accounts for the system’s known mutual orbit, arbitrary component shapes, and thermal conduction in the presence of eclipses. We obtain two local thermal-inertia values, representative of the respective shadowed areas: 21 ± 14 J s - 1 / 2 K - 1 m - 2 and 6.4 ± 1.6 J s - 1 / 2 K - 1 m - 2 . The average thermal inertia is estimated to be 20 ± 15 J s - 1 / 2 K - 1 m - 2 , potentially with significant surface heterogeneity. This first thermal-inertia measurement for a Trojan asteroid indicates a surface covered in fine regolith. Independently, we establish the presence of fine-grained (<a few μ m ) silicates on the surface, based on emissivity features near 10 and 20 μ m similar to those previously found on other Trojans. We also report V-band observations and report a lightcurve with complete rotational coverage. The lightcurve has a low amplitude of 0.070 ± 0.005 mag peak-to-peak, implying a roughly spherical shape for both components, and is single-periodic with a period ( 103.02 ± 0.40 h ) equal to the period of the mutual orbit, indicating that the system is fully synchronized. The diameters of Patroclus and Menoetius are 106 ± 11 and 98 ± 10 km , respectively, in agreement with previous findings. Taken together with the system’s known total mass, this implies a bulk mass density of 1.08 ± 0.33 g cm - 3 , significantly below the mass density of L4-Trojan asteroid (624) Hektor and suggesting a bulk composition dominated by water ice. All known physical properties of Patroclus, arguably the best studied Trojan asteroid, are consistent with those expected in icy objects with devolatilized surface (extinct comets), consistent with what might be implied by recent dynamical modeling in the framework of the Nice Model.