The role played by heat accumulation in multi-shot damage of silicon was studied. Bulk silicon samples were exposed to intense XUV monochromatic radiation of a 13.5 nm wavelength in a series of 400 femtosecond pulses, repeated with a 1 MHz rate (pulse trains) at the FLASH facility in Hamburg. The observed surface morphological and structural modifications are formed as a result of sample surface melting. Modifications are threshold dependent on the mean fluence of the incident pulse train, with all threshold values in the range of approximately 36-40 mJ/cm2. Experimental data is supported by a theoretical model described by the heat diffusion equation. The threshold for reaching the melting temperature (45 mJ/cm2) and liquid state (54 mJ/cm2), estimated from this model, is in accordance with experimental values within measurement error. The model indicates a significant role of heat accumulation in surface modification processes.