Variance is not a problem; but maximum temperature is. RF noise floor increases as operating temperature increases, and as a consequence the link budget deteriorates. As the device ages toward end of product life the sensitivity degrades. I've seen that in samples I've used.
According to a quick search, maximum operating temperature for E3131 is 45°C. Not an industrial temperature range, for sure. Storage temperature maximum is only 70°C. When storage temperature is exceeded, there will be damage that will further reduce sensitivity. I guess internal temperature rise of 25°C when powered up.
With damage, the reported signal strength may fail to track actual signal strength. You can prove damage by replacing the E3131 with an unused one and see how it behaves.
Depending on the location, and the type of surface, the ground temperatures can be very high. You can test these with infrared thermometer, or add a temperature sensor to your application, or correlate failures against hour of day and past temperatures recorded by http://bom.gov.au/
My gut feel is that it should work fine if the pillar has passive airflow inlet at least a foot above ground, but not if the pillar has at-ground airflow, no airflow or is in direct sunlight.