  The extended thermodynamics of Reissner-Nordstr\"om charged black holes in
D-dimensional anti-de Sitter spacetime has a phase structure in the (T,p) plane
that includes a line of first order phase transitions ending in a second order
transition point. For each D>=4, properties of the critical black hole at that
point are explored, motivated by the observation that in D=4 its neighbourhood
plays a core role in defining a very special class of heat engines that
asymptote to Carnot efficiency in the large charge limit. This new limit
provides a model of a novel low-temperature thermodynamic system. The double
limit of approaching the horizon while sending q large at an appropriate rate
yields a fully decoupled D-dimensional Rindler spacetime with zero cosmological
constant.
