Well, that one was remarkably easy. Take the sorted annual mean recorded temperature and see if the top result is 1998:
rmw42@pandora:~/NOAA$ cat Averages.txt | ./topyear 1163 stations had their warmest year in 1998 4985 stations did not have their warmest year in 1998 9970 stations rejected for having insufficient data
That would be a “no”, then. 19% of stations report 1998 as their warmest year, which means 81% do not. Clearly the proposition is not true.
19% is quite a lot, though, and 1998 was clearly a very warm year. Is it likely that another year scores a much higher proportion? If not, the proposition is ill-defined: there is no such thing as a warmest year for the entire planet, as different parts are warm at different times. That’s different from the proposition being false – instead the proposition is meaningless.
Possible follow-up: what does the histogram of “warmest years” look like? Would need to be careful to take account of incomplete coverage… Similarly, the Mean Reciprocal Rank of a year would be interesting to see.