A: 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:
http://ingrid.ldgo.columbia.edu/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