Using DSC scans and NMR line-shape analysis we have investigated the thermal properties of orientationally disordered crystal forming cyclohexane and benzene confined in highly ordered mesoporous materials MCM-41 and SBA-15. Phase transition temperatures and nature of the phases as a function of temperature were determined. In pores with diameters corresponding roughly to 10-30 molecular sizes (4.7 less than or equal to d less than or equal to 14.0 nm), important depressions of the melting point were observed and the confined material crystallizes only partially. The progressive melting of confined crystals detected by NMR is comparable to premelting effects usually observed in bulk molecular crystals. Here the surface of the pores plays the same role as the extended defects at the origin of premelting effects in bulk crystals. Unless in bulk crystals where premelting begins only a few degrees below the melting point, these effects spread out over a very large temperature range in confined crystals. The systematic analysis of various topology and surface interaction clearly showed that, besides the pore size, the other driving parameters for the phase transitions are the interactions between the confined fluids and the pore surface and the commensurability between the crystal symmetry and the surface structure. The melting point depression is larger in cyclohexane than in benzene due to the interaction between the T electrons of the benzene ring and the OH at the pore surface. In cyclohexane, the depression of the monoclinic to cubic transition temperature is always smaller than the melting point depression, inducing a decrease of the cubic phase temperature range with decreasing pore diameter. In 4.7 nm or narrower pores, both transitions disappear and liquid cyclohexane undergoes a glass transition even at cooling rate as small as 1 K/min. Benzene does crystallize in 4.7 nm pores but vitrifies in narrower pores. A phase diagram, presenting solid-solid-phase transition, melting and glass transition temperatures as a function of pore diameter was derived from experimental results.