In virology, temperate refers to the ability of some bacteriophages (notably coliphage λ) to display a lysogenic life cycle.
Many (but not all) temperate phages can integrate their genomes into their host bacterium's chromosome, together becoming a lysogen as the phage genome becomes a prophage.
[2] In the majority of observed switch events, stressors - such as the cell's SOS response (due to DNA damage) or a change in nutrients - induces the switch.
[3] Temperate phages can switch between a lytic and lysogenic life cycle.
[4][5][6] Here is a chart on temperate phages that are lytic and lysogenic and how they're related.