Warming or cooling from a random walk process in the temperature

A simple 3-parameter random walk model for monthly fluctuations $\triangle T$ of a temperature $T$ is introduced. Applied to a time range of 170 years, temperature fluctuations of the model produce for about 14\% of the runs warming that exceeds the observed global warming of the earth surface temperature from 1850 to 2019. On the other hand, there is a 50\% likelihood for runs of our model resulting in cooling. If a similar random walk process can be used as an effective model for fluctuations of the global earth surface temperature, effects due to internal and external forcing could be considerably over- or underestimated.