Saturn's moon Titan has a nitrogen atmosphere comparable to Earth's, with a surface pressure of 1.4 bar. Numerical models reproduce the tropospheric conditions very well but have trouble explaining the observed middle-atmosphere temperatures, composition and winds. The top of the middle-atmosphere circulation has been thought to lie at an altitude of 450 to 500 kilometres, where there is a layer of haze that appears to be separated from the main haze deck. This 'detached' haze was previously explained as being due to the co-location of peak haze production and the limit of dynamical transport by the circulation's upper branch. Here we report a build-up of trace gases over the south pole approximately two years after observing the 2009 post-equinox circulation reversal, from which we conclude that middle-atmosphere circulation must extend to an altitude of at least 600 kilometres. The primary drivers of this circulation are summer-hemisphere heating of haze by absorption of solar radiation and winter-hemisphere cooling due to infrared emission by haze and trace gases; our results therefore imply that these effects are important well into the thermosphere (altitudes higher than 500 kilometres). This requires both active upper-atmosphere chemistry, consistent with the detection of high-complexity molecules and ions at altitudes greater than 950 kilometres, and an alternative explanation for the detached haze, such as a transition in haze particle growth from monomers to fractal structures.