Where do you suggest I look for a global map of surface air temperature?

Of the datasets of which I am aware, the following one in the IRI Data Library comes closest to what you describe:

http://iridl.ldeo.columbia.edu/SOURCES/.JONES/

This gridded dataset is coarse (5 deg. by 5 deg.), but there is a climatology (1950-79) and gridded anomalies. However, I would suggest that you read through the documentation that accompanies the dataset, regarding the production of the monthly climatology and anomalies and the source of the data.

Another shorter (1958-73) climatology with a 5 deg. by 2.5 deg. resolution is located here:

/SOURCES/.OORT/.Surface/.tair/

And, ECMWF monthly gridded analyses for 1985-92 are located here:

http://ingrid.ldgo.columbia.edu/SOURCES/.ECMWF/.GGA/.t2m/

-- Michael Bell