Recent years have seen increasing attention to TCES technology owing to its potentially high energy density and suitability for long-duration storage with negligible loss, and it benefits the deployment of future net-zero energy systems. This paper provides a review of salt hydrate adsorption material-based TCES for space heating applications at ~150 °C. The incorporation of salt hydrates into a porous matrix to form composite materials provides the best avenue to overcome some challenges such as mass transport limitation and lower thermal conductivity. Therefore, a systematic classification of the host matrix is given, and the most promising host matrix, MIL-101(Cr)(MOFs), which is especially suitable for loading hygroscopic salt, is screened from the perspective of hydrothermal stability, mechanical strength, and water uptake. Higher salt content clogs pores and, conversely, reduces adsorption performance; thus, a balance between salt content and adsorption/desorption performance should be sought. MgCl2/rGOA is obtained with the highest salt loading of 97.3 wt.%, and the optimal adsorption capacity and energy density of 1.6 g·g−1 and 2225.71 kJ·kg−1, respectively. In general, larger pores approximately 8–10 nm inside the matrix are more favorable for salt dispersion. However, for some salts (MgSO4-based composites), a host matrix with smaller pores (2–3 nm) is beneficial for faster reaction kinetics. Water molecule migration behavior, and the phase transition path on the surface or interior of the composite particles, should be identified in the future. Moreover, it is essential to construct a micromechanical experimental model of the interface.