Context : Highly-collimated outflows are believed to be the earliest stage in outflow evolution, so their study is essential for understanding the processes driving outflows. The BHR71 Bok globule is known to harbour such a highly-collimated outflow, which is powered by a protostar belonging to a protobinary system. Aims : We aimed at investigating the interaction of collimated outflows with the ambient molecular cloud by using molecular tracers. Methods : We mapped the BHR71 highly-collimated outflow in CO(3-2) with the APEX telescope, and observed several bright points of the outflow in the molecular transitions CO(4-3), 13CO(3-2), C18O(3-2), and CH3OH(7-6). We use an LVG code to characterise the temperature enhancements in these regions. Results : In our CO(3-2) map, the second outflow driven by IRS2, which is the second source of the binary system, is completely revealed and shown to be bipolar. We also measure temperature enhancements in the lobes. The CO and methanol LVG modelling points to temperatures between 30 and 50K in the IRS1 outflow, while the IRS2 outflow seems to be warmer (up to 300K).