Cytosine methylase that recognizes the double-stranded sequence 5'-GC(A/T)GC-3', methylates C-5 position of the second cytosine on both strands, and protects the DNA from cleavage by the ApeKI endonuclease. a 2'-deoxycytidine in DNA + S-adenosyl-L-methionine = a 5-methyl-2'-deoxycytidine in DNA + H(+) + S-adenosyl-L-homocysteine Optimum temperature is between 70-90 degrees Celsius. Highly thermostable. 34% of the activity of the unheated sample after incubation at 90 degrees Celsius for 10 hours. Lowest activity detected at 10 degrees Celsius. This protein may be useful as an epigenetic editing tool due to its high thermostability. Belongs to the class I-like SAM-binding methyltransferase superfamily. C5-methyltransferase family.