Catalyzes the methylation of lysine residues in target proteins, using S-adenosyl-L-methionine (SAM) as the methyl donor. Exhibits broad substrate specificity, being able to methylate the crenarchaeal chromatin protein Cren7 primarily at 'Lys-11', 'Lys-16' and 'Lys-31', as well as a number of recombinant Sulfolobus proteins in vitro. Methylates lysine residues in a rather sequence-independent manner. L-lysyl-[protein] + S-adenosyl-L-methionine = H(+) + N(6)-methyl-L-lysyl-[protein] + S-adenosyl-L-homocysteine Optimum temperature is about 60 degrees Celsius. Is active over a wide temperature range, from 25 to 90 degrees Celsius. Has half-lives of about 30 and 10 minutes at 80 and 90 degrees Celsius, respectively. Monomer. Seems to be expressed at similar protein levels when grown at 75 or 85 degrees Celsius, or in the exponential or the stationary phase. Belongs to the class I-like SAM-binding methyltransferase superfamily.