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Nanothermal-expansion of poly(ethylene-co-vinylacetate), EVA, and poly(methyl methacrylate), PMMA, in the form of films was measured to finally obtain linear coefficients of thermal expansion, CTEs. The simple deflection of a cantilever in an atomic force microscope, AFM, was used to monitor thermal expansions at the nanoscale. The influences of: (a) the structure of EVA in terms of its composition (vinylacetate content) and (b) the size of PMMA chains in terms of the molecular weight were studied. To carry out this, several polymer samples were used, EVA copolymers with different weight percents of the vinylacetate comonomer (12, 18, 25 and 40%) and PMMA polymers with different weight average molecular weights (33.9, 64.8, 75.600 and 360.0 kg mol(-1)). The dependencies of the vinyl acetate weight fraction of EVA and the molecular weight of PMMA on their corresponding CTEs were analyzed to finally explain them using new, intuitive and very simple models based on the rule of mixtures. In the case of EVA copolymers a simple equation considering the weighted contributions of each comonomer was enough to estimate the final CTE above the glass transition temperature. On the other hand, when the molecular weight dependence is considered the free volume concept was used as novelty. The expansion of PMMA, at least at the nanoscale, was well and easily described by the sum of the weighted contributions of the occupied and free volumes, respectively.