SUMMARY To date, no published study has assessed the full physiological scope of a marine invertebrate species with respect to both temperature and hydrostatic pressure. In this study, adult specimens of the shallow-water shrimp species Palaemonetes varians were subjected to a temperature/pressure regime from 5 to 30°C and from 0.1 to 30 MPa. The rate of oxygen consumption and behaviour in response to varying temperature/pressure combinations were assessed. Rates of oxygen consumption were primarily affected by temperature. Low rates of oxygen consumption were observed at 5 and 10°C across all pressures and were not statistically distinct (P=0.639). From 10 to 30°C, the rate of oxygen consumption increased with temperature; this increase was statistically significant (P<0.001). Palaemonetes varians showed an increasing sensitivity to pressure with decreasing temperature; however, shrimp were capable of tolerating hydrostatic pressures found outside their normal bathymetric distribution at all temperatures. ‘Loss of equilibrium’ (LOE) in ≥50% of individuals was observed at 11 MPa at 5°C, 15 MPa at 10°C, 20 MPa at 20°C and 21 MPa at 30°C. From 5 to 20°C, mean levels of LOE decreased with temperature; this was significant (P<0.001). Low mean levels of LOE were observed at 20 and 30°C and were not distinct (P=0.985). The physiological capability of P. varians to tolerate a wide range of temperatures and significant hydrostatic pressure is discussed.