In the context of a numerical study about mid-infrared receivers based on a metal-insulator-metal junction, we study how a top multilayer of graphene is capable to remove heat from the thin metal layer in which the laser impinges on. Due to its extremely high thermal conductivity, the graphene film (made of several layers) extracts the heat and injects it inside bulky lateral metal paddings of the receiver. Therefore, the lateral metal contacts not only detect the electromagnetic field transforming it into a current through this quantum diode, but they can also help to drain the heat. A metal-insulator-metal junction, which combines Kretschmann illumination and a distributed light on the junction (or are illuminated through a grating), allows introducing the electromagnetic field into the junction, biasing in this manner the insulator all along its entire length. The main challenge is the relationship between the insulator thickness and the electromagnetic wavelength. In the mid-infrared region, the insulator thickness of a few nanometers is several orders of magnitude under the diffraction limit, and the electromagnetic field cannot penetrate directly into the structure. In this way, the described technique delivers the infrared radiation into the junction by means of surface-plasmon-polariton traveling wave (SPP-TW). Therefore, a right illumination improves the diode responsivity considerably. However, rectification demands an extremely asymmetrical current-voltage curve. A layered metal-graphene-insulator-metal makes this feasible especially when an SPP-TW, between the graphene and the insulator, establishes a Seebeck effect resulting in the desired asymmetric characteristic. When sampling, the rectified direct tunneling current is desirable to avoid thermionic emission (inherently slow), as well as to induce the SPP-TW in a better form from the outside of the junction. A cooling mechanism that preserves a high electric conductivity on the top metal contact is required. In this theoretical work, we performed a simulation study of how a sheet of graphene is able to enhance the thermal behavior of the receiver under study.