High values of the Hurst exponent of H=0.66±0.05 for deseasonalized monthly mean surface temperatures in the sample period 1850-2015 suggest persistence and long term memory in the temperature time series. Such Hurst phenomena have been observed in the stochastic processes of nature in the area of hydrology (Hurst) and also in the proxy record of annual mean surface temperature at a millennial time scale (Barnett). Our study suggests that these patterns may also exist in deseasonalized monthly means of the measured temperature record in the post industrial era, a period that is normally associated with global warming and climate change.