In this work, the effect of the counterion valence on the behavior Of thermo-sensitive gels and microgels is studied through Computer simulations. The polyelectrolyte gel is described Within a bead-spring model and ions are explicitly considered. The thermo-shrinking behavior is simulated With the help of a phenomenological solvent-mediated polymer-polymer interaction that captures the essential features of experimental swelling data. Our results show that the Swelling effect of Multivalent species is smaller than in the case of monovalent counterions and therefore lower temperatures are required : for the hydrophobic collapse of the polymer network. The reduction of the number of counterions when their valence is increased is responsible to a great extent for the smaller swelling effect. However, our simulations also reveal other mechanisms involved but completely ignored by most of the Flory-Rhener-inspired theories. For instance, the strong electrostatic interaction between multivalent counterions and the charged beads of the network reduces the pressure exerted by them. In addition, a bridging effect induced by these ions enhances hydrophobic interactions, which also contributes to the collapse of the gel.