While some DNA methylation variants are transgenerationally stable in plants, DNA methylation modifications that are specifically induced by environmental exposure are typically transient and subject to resetting in germ lines, limiting the potential for transgenerational epigenetics stress memory. Asexual reproduction circumvents germlines, and may be more conducive to long-term memory and inheritance of epigenetic marks. This, however, has been poorly explored. Taking advantage of the rapid clonal reproduction of the common duckweed Lemna minor, we tested the hypothesis that a long-term, transgenerational stress memory from exposure to high temperature can be detected in DNA methylation profiles. Using a reduced representation bisulfite sequencing approach (epiGBS), we show that high temperature stress induces DNA hypermethylation at many cytosines in CG and CHG contexts but not in CHH. In addition, a subset of the temperature responsive CHG cytosines, showed differential DNA methylation between in lineages exposed to 30C and 24C, 3-12 clonal generations after subsequent culturing in a common environment, demonstrating a memory effect of stress that persists over many clonal generations and that is reflected in DNA methylation. Structural annotation revealed that this memory effect in CHG methylation was enriched in TEs. We argue that the observed epigenetic stress memory is likely caused by stable transgenerational persistence of high temperature-induced DNA methylation variants across multiple clonal generations. To the extent that such epigenetic memory has functional consequences for gene expression and phenotypes, this result suggests potential for long-term modulation of stress responses in asexual plants and vegetatively propagated crops.