Context. Supernovae remnants (SNRs) represent a major source of feedback from stars on the interstellar medium of galaxies. During the latest stage of supernova explosions (which lasts 10–100 kyr), shock waves produced by the initial blast modify the chemistry of gas and dust, inject kinetic energy in the surroundings, and may alter star formation characteristics. Simultaneously, γ-ray emission is generated by the interaction between the ambient medium and cosmic rays, in particular those locally accelerated in the early stages of the explosion.Aims. We aim to estimate the total molecular mass, local density, and total column density of H2 and the temperature structure in a shocked clump interacting with the supernova remnant IC443 located in a region where cosmic rays interact with the interstellar medium. Measuring the mass of the dense and neutral component of the medium is a prerequisite to understanding the chemistry, energetics, and GeV to TeV γ-ray emission.Methods. Assuming that the emission of H2 pure rotational lines is produced by a collection of gas layers with variable temperature, we compared Spitzer/IRS emission maps for the ν = 0–0 S(0) to S(7) lines with a thermal admixture model. Our description is based on a power-law distribution of thermalized components with temperatures varying between Tmin = 25 K and Tmax = 1500 K.Results. Our thermal admixture model allows the level populations of H2 to be described by a power-law distribution dN = ΛT−ΓdT, with Γ ~ 2.2−4.7. We measured a total mass MH2 = 220−80+110 M⊙ across the Spitzer/IRS field of observations.Conclusions. Our analysis shows that an estimate of the cold molecular gas temperature is paramount to accurately constraining the H2 mass, although the mass remains affected by significant uncertainties due to the assumptions on the gas temperature distribution.