Is the world's average temperature warming? Yes, it is.
The data is the Combined Land-Surface Air and Sea-Surface Water Temperature Anomalies (Land-Ocean Temperature Index, LOTI), Global-mean monthly, seasonal, and annual means, 1880-present
The chart is a line plot of differences in annual land-ocean average temperature from the average for the base period 1951-1980 global mean temperature index, 1880 to present. The dotted blue line is the annual mean and the solid red line is the five-year mean, calculated with a Lowess function.