Responsive poly-N-isopropylacrylamide-based microgels are commonly used as model colloids with soft repulsive interactions. It has been shown that the microgel-microgel interaction in solution can be easily adjusted by varying the environmental parameters, e.g., temperature, pH, or salt concentration. Furthermore, microgels readily adsorb to liquid-gas and liquid-liquid interfaces forming responsive foams and emulsions that can be broken on-demand. In this work, we explore the interactions between microgel monolayers at the air-water interface and a hard colloid in the water. Force-distance curves between the monolayer and a silica particle were measured with the Monolayer Particle Interaction Apparatus. The measurements were conducted at different temperatures and lateral compression, i.e., different surface pressures. The force-distance approach curves display long-range repulsive forces below the volume phase transition temperature of the microgels. Temperature and lateral compression reduce the stiffness of the monolayer. The adhesion increases with temperature and decreases with a lateral compression of the monolayer. When compressed laterally, the interactions between the microgels are hardly affected by temperature, as the directly adsorbed microgel fractions are nearly insensitive to temperature. In contrast, our findings show that the temperature-dependent swelling of the microgel fractions in the aqueous phase strongly influences the interaction with the probe. The microgel monolayer changes from a soft to a hard repulsive interface.