Cultural Heritage is a vital socioeconomic driver that must contend with works of art continuously exposed to degradation processes, which are further exacerbated by climate change. Aged coatings, varnishes, and soil can compromise the appearance of artworks, preventing their preservation and valorization. In response, soft matter and colloidal systems, such as nanostructured cleaning fluids (NCFs), have proved to be valuable solutions for safely and effectively cleaning works of art. Here, a novel cleaning system is proposed, for the first time employing microgels of poly(-isopropylacrylamide) (PNIPAM) with surface chains of oligoethylene glycol methyl ether methacrylate (OEGMA) to favor shear deformation by lubrication. These microgels are loaded with NCFs featuring "green" solvents and different kinds of bio-derived or petroleum-based surfactants (non-ionic, zwitterionic). Rheological characterization of the combined systems highlighted a sharp transition from solid to liquid-like state in the 21-24 °C range when the zwitterionic surfactant dodecyldimethylamine oxide was used; the system displays a solid-like behavior at rest but flows easily at intermediate strains. At slightly higher temperature (>24 °C), an inversion of the G', G″ values was observed, leading to a system that behaves as a liquid. Such control of rheological behavior is significant for feasible and complete removal of soiled polymer coatings from textured ceramic surfaces, which are difficult to clean with conventional gels, without leaving residues. These results position the PNIPAM-OEGMA microgels as promising cleaning materials for the conservation of Cultural Heritage, with possible applications also in fields where gelled systems are of interest (pharmaceutics, cosmetics, detergency, etc.).