Context: Near-Earth asteroid-comet transition object 107P/ (4015) Wilson-Harrington is a possible target of the joint European Space Agency (ESA) and Japanese Aerospace Exploration Agency (JAXA) Marco Polo sample return mission. Physical studies of this object are relevant to this mission, and also to understanding its asteroidal or cometary nature. Aims: Our aim is to obtain significant new constraints on the surface thermal properties of this object. Methods: We present mid-infrared photometry in two filters (16 and 22 μm) obtained with NASA's Spitzer Space Telescope on February 12, 2007, and results from the application of the Near Earth Asteroid Thermal Model (NEATM). We obtained high S/N in two mid-IR bands allowing accurate measurements of its thermal emission. Results: We obtain a well constrained beaming parameter (η = 1.39±0.26) and obtain a diameter and geometric albedo of D = 3.46±0.32 km, and pV = 0.059±0.011. We also obtain similar results when we apply this best-fitting thermal model to single-band mid-IR photometry reported by Campins et al. (1995, P&SS, 43, 733), Kraemer et al. (2005, AJ, 130, 2363) and Reach et al. (2007, Icarus, 191, 298). Conclusions: The albedo of 4015 Wilson-Harrington is low, consistent with those of comet nuclei and primitive C-, P-, D-type asteorids. We establish a rough lower limit for the thermal inertia of W-H of 60 Jm-2s-0.5 K-1 when it is at r = 1 AU, which is slightly over the limit of 30 Jm-2 s-0.5 K-1 derived by Groussin et al. (2009, Icarus, 199, 568) for the thermal inertia of the nucleus of comet 22P/Kopff.