  We present highly resolved measurements of the near-wall temperature field in
thermally driven convection at a rough surface. Our measurements have been
undertaken in a very large experimental facility called the "Barrel of
Ilmenau". They provide a unique insight into the local transport process at the
interface between a hot solid surface and a surrounding fluid. In order to
probe the near-wall temperature field, we used a tiny micro-thermistor of 130
$\mu$m in diameter and 330 $\mu$m in length with a response time $\tau_{70}$ of
less than 150 ms. This sensor is forty times smaller than the thickness of the
boundary layer, and it permits a resolution better than the typical Kolmogorov
micro-scales that appear in our experiment. We demonstrate that the heat flux
enhancement generally observed at rough surfaces, basically results from an
increase of the local heat transfer coefficient at the top of the roughness
elements. We also shed light on the detailed mechanism of the transition in the
scaling of the global heat transfer relation $Nu\sim Ra^{\gamma}$ that has been
observed beyond a critical Ra number $Ra_c$. In turbulent Rayleigh-B\'enard
convection with rough surfaces, it already appears at $Ra_c\approx 10^{10}$
[Tisserand et al.{\em Phys. Fluids \/} 23, 015105(2011)] while, for smooth
plates, it has been predicted at $Ra_c\approx 10^{14}$ [[Grossmann \& Lohse
{\em Phys. Rev. Lett.\/} {\bf 86}, 3316(2001)]. We found this transition at
rough surfaces to be attributed to an earlier laminar-turbulent transition of
the boundary layer at the top of the roughness elements as well as to a
modification of the temperature field in between the obstacles.
