While collisionally excited lines in H ii regions allow one to easily probe the chemical composition of the interstellar medium in galaxies, the possible presence of important temperature fluctuations casts some doubt on the derived abundances. To provide new insights into this question, we have carried out a detailed study of a giant H ii region, H 1013, located in the galaxy M101, for which many observational data exist and which has been claimed to harbour temperature fluctuations at a level of t2 = 0.03-0.06. We have first complemented the already available optical observational datasets with a mid-infrared spectrum obtained with the Spitzer Space Telescope. Combined with optical data, this spectrum provides unprecedented information on the temperature structure of this giant H ii region. A preliminary analysis based on empirical temperature diagnostics suggests that temperature fluctuations should be quite weak. However, only a detailed photoionization analysis taking into account the geometry of the object and observing apertures can make a correct use of all the observational data. We have performed such a study using the pyCloudy package based on the photoionization code Cloudy. We have been able to produce photoionization models constrained by the observed Hβ surface brightness distribution and by the known properties of the ionizing stellar population than can account for most of the line ratios within their uncertainties. Since the observational constraints are both strong and numerous, this argues against the presence of significant temperature fluctuations in H 1013. The oxygen abundance of our best model is 12 + log O/H = 8.57, as opposed to the values of 8.73 and 8.93 advocated by Esteban et al. (2009, ApJ, 700, 654) and Bresolin (2007, ApJ, 656, 186), respectively, based on the significant temperature fluctuations they derived. However, our model is not able to reproduce the intensities of the oxygen recombination lines observed by Esteban et al., as well as the very low Balmer jump temperature inferred by Bresolin. We have argued that the latter might be in error, due to observational difficulties. On the other hand, the discrepancy between model and observation as regards the recombination lines cannot be attributed to observational uncertainties and requires an explanation other than temperature fluctuations.