Experiments have been carried out in the JET tokamak in order to determine the critical iontemperature inverse gradient length (R/LTi =R|∇Ti|/Ti) for the onset of Ion Temperature Gradientmodes and the stiffness of Ti profiles with respect to deviations from the critical value. The existenceof a threshold in R/LTi has been assessed and its value found in close agreement with linear GS2gyro-kinetic calculations. The ion stiffness level is high and keeps R/LTi close to the linear thresholdirrespective of the amount of core ion heating. This finding is not in agreement with non-linear GS2calculations, yielding significantly higher R/LTi values than the linear threshold. Comparison ofplasmas with different values of toroidal rotation indicates a significant increase in R/LTi in rotatingplasmas. Various observations allow to conclude that such increase is mainly due to a decrease ofthe stiffness level with increasing rotation, rather than to a mere up-shift of the threshold, as commonlypredicted by theory. This finding has implications on the interpretation of present day experimentalresults on the effect of rotation on confinement as well as on extrapolations to future machines.