The deposition of high molecular weight paraffins on the inner wall of sub- sea production and transportation pipelines continues to be a critical operational problem faced by the petroleum industry. The accumulation of the deposited material on the inner wall of the lines may lead to increased pumping power, decreased flow rate, or even the total blockage of the line, with an accompanying loss of production and capital investment. In the present work, a critical review of the literature on wax deposition was conducted and concluded that there is not enough experimental evidence to determine which are the relevant mechanisms responsible for wax deposition. Based on the findings of the literature search, a research program was initiated with the aim of identifying the relative importance of the wax deposition mechanisms. To this end, simple, basic experiments were designed and complemented by numerical simulations. The present paper is part of this ongoing research program and reports on experiments on deposition in cavities containing a stagnant solution of paraffin and solvent and submitted to a transverse temperature gradient. The experiments yielded temporal distributions of paraffin deposits. A molecular diffusion- based model underestimated the evolution of the deposit thickness for the stagnant cavity. The results obtained were not sufficient to corroborate the widely accepted hypothesis that the wax deposition process is controlled by molecular diffusion.