Metallic Phase Change Materials (PCMs), based on solid-liquid transitions, represents one of the most promising technologies for efficient Thermal Energy Storage (TES), due to their superior thermal conductivity and energy storability per unit volume, but suffer of limited solutions for their handling at the molten state. The use of Miscibility Gap Alloys (MGAs) allows to manage PCM volume expansion and keep it confined when molten, preventing interaction with the environment. A relevant example is provided by the Al-Sn system, where Al covers the role of the high-temperature stable and highly thermal-conductive passive matrix and Sn the active PCM. The alloy can thus be considered a Composite PCM (C-PCM). The response fastness of these systems depends on their thermal diffusivity, subjected to abrupt variations under the presence of discontinuities and damages. In this sense, the authors investigated the possibility to employ molten Sn mobility in a potentially damaged C-PCM for self-healing purposes, aimed to restore, at least partially, the material continuity and thus its thermal diffusivity. Exudation heat treatments above the melting temperature of Sn were performed on sets of Al-40%wt. Sn metallic composites, produced either with powder metallurgy or liquid metal routes, in order to quantify and assess the mobility of the Sn under simulated operating conditions. Exudation tests assess Simple Mixed powders and liquid metal routes sample as the ones with the highest healing potential. Al dissolution and re-deposition was established by EDS analyses as one of the principal Sn mobility mechanisms. Laser Flash Analysis tests, as well as microstructural investigations, were performed on the samples before and after both healing-focused and simulated service heat treatments to evaluate the changes of thermal diffusivity. Healing-focused treatment at 250°C for 1 hour generally displayed a moderate thermal diffusivity recovery and simulated service by shorter cycles between 170°C and 270°C slightly reduce it. The beneficial role of healing focused heat treatments at 250°C for 1 hour suggests that the presence of fully molten Sn phase during service for relatively long time could be beneficial for functional healing. The requirements of suitable Al-Sn microstructures for self-healing purposes, granting at the same time the C-PCM functionalities, i.e., thermal energy storage and form-stability, were set.