Rubber　has　strong　nonlinear　viscoelastic　behavior.　Under　the　periodically　changing　external　forces,　it　show　deformation　hysteresis,　mechanical　loss　and　heat　generation.　In　this　work,　a　pair　of　extruding　and　rotating　steel-rubber　rollers　was　researched.　Stress　relaxation　data　at　different　temperatures　were　obtained　through　dynamic　thermomechanical　analysis　experiments.　A　thermo-viscoelastic　rubber　constitutive　model　with　temperature　factor　was　obtained　by　combining　the　generalized　Maxwell　model　where　parameters　of　rubber　viscoelastic　were　fitted　with　Prony　series.　Then,　the　temperature　experiment　of　structure　was　conducted　on　the　experimental　platform.　Based　on　thermo-viscoelastic　constitutive　model,　simulation　and　analysis　of　temperature　distribution　of　steel-rubber　roller　was　obtained.　The　results　of　experimental　data　were　consistent　with　simulation　results.　Further,　the　rubber　constitutive　models　of　pure　elasticity,　the　superposition　of　elasticity　and　viscoelasticity　with　non-temperature　factors,　the　superposition　of　elasticity　and　viscoelasticity　with　temperature　factors　were　simulated　respectively.　The　results　show　that　the　third　model　was　more　consistent　with　the　actual　experimental　results,　which　verifies　the　accuracy　of　constitutive　model　building　by　this　work.　Through　numerical　comparison　and　analysis,　it　was　proved　that　viscoelastic　hysteretic　heat　generation　is　an　indispensable　source　of　heat　generation　in　rubber　structure　movement.　©　Published　under　licence　by　IOP　Publishing　Ltd.