In budding yeast, Set2 catalyzes di- and trimethylation of H3K36 (H3K36me2 and H3K36me3) via an interaction between its Set2-Rpb1 interaction (SRI) domain and C-terminal repeats of RNA polymerase II (Pol2) phosphorylated at Ser2 and Ser5 (CTD-S2,5-P). H3K36me2 is sufficient for recruitment of the Rpd3S histone deacetylase complex to repress cryptic transcription from transcribed regions. In fission yeast, Set2 is also responsible for H3K36 methylation, which represses a subset of RNAs including heterochromatic and subtelomeric RNAs, at least in part via recruitment of Clr6 complex II, a homolog of Rpd3S. Here, we show that CTD-S2P-dependent interaction of fission yeast Set2 with Pol2 via the SRI domain is required for formation of H3K36me3, but not H3K36me2. H3K36me3 silenced heterochromatic and subtelomeric transcripts mainly through post-transcriptional and transcriptional mechanisms, respectively, whereas H3K36me2 was not enough for silencing. Clr6 complex II appeared not to be responsible for heterochromatic silencing by H3K36me3. Our results demonstrate that H3K36 methylation has multiple outputs in fission yeast; these findings provide insights into the distinct roles of H3K36 methylation in metazoans, which have different enzymes for synthesis of H3K36me1/2 and H3K36me3.