External temperature change has been shown to modify epigenetic patterns, such as DNA methylation, which regulates gene expression. DNA methylation is heritable, and as such provides a mechanism to convey environmental information to subsequent generations. Studies on epigenetic response to temperature increase are still scarce in wild mammals, even more so studies that compare tissue-specific epigenetic responses. Here, we aim to address differential epigenetic responses on a gene and gene pathway level in two organs, liver and testis. We chose these organs, because the liver is the main metabolic and thermoregulation organ, and epigenetic modifications in testis are potentially transmitted to the F2 generation. We focused on the transmission of DNA methylation changes to naive male offspring after paternal exposure to an ambient temperature increase of 10 °C, and investigated differential methylated regions of sons sired before and after the paternal exposure using Reduced Representation Bisulfite Sequencing. We detected both a highly tissue-specific epigenetic response, reflected in genes involved in organ-specific metabolic pathways, and a more general regulation of single genes epigenetically modified in both organs. We conclude that genomes are context-specifically differentially epigenetically regulated in response to temperature increase. These findings emphasize the epigenetic relevance in cell differentiation, which is essential for the specific function(s) of complex organs, and is represented in a diverse molecular regulation of genes and gene pathways. The results also emphasize the paternal contribution to adaptive processes.