  New high-resolution dissociative recombination rate coefficients of
rotationally cool and hot H3+ in the vibrational ground state have been
measured with a 22-pole trap setup and a Penning ion source, respectively, at
the ion storage ring TSR. The experimental results are compared with
theoretical calculations to explore the dependence of the rate coefficient on
ion temperature and to study the contributions of different symmetries to probe
the rich predicted resonance spectrum. The break-up energy was investigated by
fragment imaging to derive internal temperatures of the stored parent ions
under differing experimental conditions. A systematic experimental assessment
of heating effects is performed which, together with a survey of other recent
storage-ring data, suggests that the present rotationally cool rate-coefficient
measurement was performed at 380^{+50}_{-130} K and that this is the lowest
rotational temperature so far realized in storage-ring rate-coefficient
measurements on H3+. This partially supports the theoretical suggestion that
higher temperatures than assumed in earlier experiments are the main cause for
the large gap between the experimental and theoretical rate coefficients. For
the rotationally hot rate-coefficient measurement a temperature of below 3250K
is derived. From these higher-temperature results it is found that increasing
the rotational ion temperature in the calculations cannot fully close the gap
between the theoretical and experimental rate coefficients.
