Studies of handedness suggest a relationship between hemispheric specialisation and emotional processing. Recently measures of lateralised tympanic membrane temperature (TMT) have identified similar relationships (i.e., the left hemisphere is involved in approach behaviour and the right hemisphere avoidance behaviour). In the present study we examined lateralised changes in TMT in response to social interaction in 10 Garnett's bushbabies. Additionally, we examined whether handedness could be used as a predictor of approach-avoidance tendencies. We found a positive association between temperature change and both allogrooming and affiliative approach. Social behaviour did not differ between right- and left-handed bushbabies. These findings are discussed in terms of existing theories of asymmetric emotional processing. Overall, the data suggest that there is a left hemisphere specialisation for processing approach-related behaviours, which is consistent with existing models of lateralised emotional processing. Our data also indicate that TMT is a reliable, cost-effective measure of cerebral activation that is less invasive and more practical than alternative measures such as EEG, PET, and fMRI.