We report highly resolved temperature measurements in turbulent Rayleigh–Bénard convection in air at a fixed Prandtl number Pr = 0.7. Extending our previous work (du Puits et al 2007 J. Fluid Mech. 572 231–54), we carried out measurements at various aspect ratios while keeping the Rayleigh number constant. We demonstrate that the temperature field inside the convective boundary layers of both horizontal plates is virtually independent on the global flow pattern accompanying the variation in the aspect ratio. Thanks to technical upgrades of the experimental facility as well as a significant improvement of the accuracy and reliability of our temperature measurement — and unlike in our previous work — we find that the measured profiles of the time-averaged temperature field neither follow a clear power-law trend nor fit a linear or a logarithmic scaling over a significant fraction of the boundary-layer thickness. Analyzing the temperature data simultaneously acquired at both horizontal plates, various transitions in the cross-correlation and the auto-correlation function of the temperature signals are observed while varying the aspect ratio Γ. These transitions might be associated with a change in the global flow pattern from a single-roll mode at Γ = 1 toward a double- or a multi-roll mode pattern at higher aspect ratios.