Mice selectively bred for high methamphetamine (MA) drinking (MAHDR), compared with mice bred for low MA drinking (MALDR), exhibit greater sensitivity to MA reward and insensitivity to aversive and hypothermic effects of MA. Previous work identified the trace amine‐associated receptor 1 gene (Taar1) as a quantitative trait gene for MA intake that also impacts thermal response to MA. All MAHDR mice are homozygous for the mutant Taar1 m1J allele, whereas all MALDR mice possess at least one copy of the reference Taar1 + allele. To determine if their differential sensitivity to MA‐induced hypothermia extends to drugs of similar and different classes, we examined sensitivity to the hypothermic effect of the stimulant cocaine, the amphetamine‐like substance 3,4‐methylenedioxymethamphetamine (MDMA), and the opioid morphine in these lines. The lines did not differ in thermal response to cocaine, only MALDR mice exhibited a hypothermic response to MDMA, and MAHDR mice were more sensitive to the hypothermic effect of morphine than MALDR mice. We speculated that the μ‐opioid receptor gene (Oprm1) impacts morphine response, and genotyped the mice tested for morphine‐induced hypothermia. We report genetic linkage between Taar1 and Oprm1; MAHDR mice more often inherit the Oprm1 D2 allele and MALDR mice more often inherit the Oprm1 B6 allele. Data from a family of recombinant inbred mouse strains support the influence of Oprm1 genotype, but not Taar1 genotype, on thermal response to morphine. These results nominate Oprm1 as a genetic risk factor for morphine‐induced hypothermia, and provide additional evidence for a connection between drug preference and drug thermal response.