This communication presents global statistics of daily mean temperature changes as a function of previous day temperature anomaly. The relationship obtained clearly exhibits properties of response functions: the larger the anomaly, the larger the expected magnitude of temperature change backward to the long-term average value. Worldwide statistics reveals that this temperature response function is inherently nonlinear and climate specific. However the central part around the origin can be approximated well by a linear fit. At a large number of geographic locations, the intercepts have small offsets toward nonzero values, and these offsets are geographically correlated. We show that one possible reason is a marked asymmetry of temperature fluctuations, that is warming steps have significantly higher frequencies and lower average magnitudes than those of cooling steps, almost everywhere. These two opposing effects could result in stationary fluctuations around an annual cycle, however, our statistics clearly indicates the presence of global warming.