When I did the performance driving school, we had tire pressure warning lights going off right and left due to the stress we were placing on the tires.
31C isn't all that hot, really. It's been above 34C here and no dash warning. I did set it off when spring went to summer. I had aired up my tires just before the temp change and the increase in ambient temperature set off the sensor. Adjusted pressures and it's been good since. If you checked the pressures while cold and they're ok, just reset the warning.