C680 Captain reported receiving a 'BATT OTEMP L' warning message during takeoff resulting in a return to the departure airport for an overweight landing.

Narrative

Shortly after takeoff from ZZZ; the red 'BATT OTEMP L' CAS (Crew Alert System) message displayed. We performed the immediate action items and ran the QRC and QRH. At that time; the battery temperature was 68 C. It briefly went up to 70 C before beginning to cool. We coordinated with ZZZ Departure for a return to ZZZ and [requested priority handling]. I notified the owner over the PA that we were returning to ZZZ 'out of an abundance of caution'. We discussed the fact that we were landing overweight and agreed it was better to land immediately rather than delaying our return to burn off fuel. After touchdown; we cleared Runway X at Taxiway 1. We asked ARFF (Airport Rescue and Firefighting) to visually inspect the exterior of the aircraft near the left wing root where the left battery compartment is located. ARFF requested we shut down the left engine. After confirming the left battery temperature had substantially decreased and receiving the all clear from ARFF; FBO tugged the aircraft to FBO south. Afterwards; I spoke with the owner. He was very understanding of the situation and grateful for our safety culture.