Spreading of ink outside the desired printed area is one of the major limitations of microcontact printing (mu-CP) with alkanethiol self-assembled monolayers (SAMs) on gold. We use molecular dynamics (MD) computer simulations to quantify the temperature and concentration dependence of hexadecanethiol (HDT) ink spreading on HDT SAMs, modeling 18 distinct printing conditions using periodic simulation cells of similar to 7 nm edge length and printing conditions ranging from 7 ink molecules per cell at 270 K to 42 ink molecules per cell at 371 K. The computed alkanethiol ink diffusion rates on the SAM are of the same order of magnitude as bulk liquid alkanethiol diffusion rates at all but the lowest ink concentrations and highest temperatures, with up to 20-30 times increases in diffusion rates at the lowest concentration-highest temperature conditions. We show that although alkanethiol surfaces are autophobic, autophobicity is not enough to pin the ink solutions on the SAM, and so any overinking of the SAM will lead to spreading of the printed pattern. Comparison of experimental and calculated diffusion data supports an interpretation of pattern broadening as a mixture of spreading on fully and partially formed SAMs, and the calculated spreading rates establish some of the fundamental limitations of mu-CP in terms of stamp contact time and desired pattern width.