In the past decade, new tools have been offered to the system designers in terms of thermal and mechanical modeling. In addition to an overwhelming increase of computer capabilities, these tools are now mature enough to drive the design of complex astronomical instruments, in particular if these instruments have to be cooled. This is the case of WIRCam, the new wide-field infrared camera to be installed on the CFHT in Hawaii on the Mauna Kea summit. This camera uses four 2Kx2K Rockwell Hawaii-2RG infrared detectors and includes 2 optical barrels and 2 filter wheels. This camera is mounted at the prime focus of the 3.6m CFHT telescope. The mass to be cooled is close to 100 kg. The camera will use a Gifford Mac-Mahon closed-cycle cryo-cooler in order to avoid strenuous daily re-fillings on the telescope due to the camera location. This paper will present the thermal-mechanical model of the camera using Finite-Element Analysis under the I-deas software. The capabilities of the I-deas thermal module (TMG) will be demonstrated for our particular application: including conduction, radiation and free-convection management, variations of the cooling power and thermal characteristics of the materials as a function of the temperature, and studies in permanent regime and transient analysis. The hypotheses used for the thermal model are explained and results of the model are shown to explain the choice of the cryo-cooler. Predicted performances (cooling down time, warm-up time, and mechanical deformations) are presented and compared to measurements. All these models were carried out using a normal PC laptop running I-deas/TMG.