Recurring Slope Lineae (RSL) are dark linear recurrent features which incrementally lengthen and fade each year on Martian slopes. Their activity during warmest seasons rises the question of modern martian water related process. To investigate this question, this study focuses on the thermal context of slopes hosting RSL. The paper presents a numerical study of surface and subsurface temperatures at high spatial resolution (1 m/pix) of three well-described RSL sites: Palikir Crater, Coprates Chasma and Rauna Crater. We then compare our local thermal simulations to quantitative measurements of the length and timing of RSL lengthening and fading in these three sites. We underline that RSL sites surface temperatures are poorly correlated with RSL morphology's changes. Indeed, lineae lengthening occurs while surface temperature are under the melting point of pure water (273 K) for at least two sites: Coprates Chasma and Rauna Crater, for two different sets of surface physical properties. We also highlight the significant differences in temperature range while lengthening occurs for all the sites, from ~220 K in Coprates Chasma site to a maximum of ~300 K in Palikir Crater. RSL are sometimes associated with signals in topography, involving significant heating variations of the surface, which can yield to the formation of local winds. Facing the thermal inconsistency between wet triggering processes and RSL reported activity, we suggest that RSL are more probably dry processes.