We demonstrate a direct approach to investigate heat transport in the fractional quantum Hall regime. At a filling factor of ν=4/3, we inject power at quantum point contacts and detect the related heating from the activated current through a quantum dot. The experiment reveals a chargeless heat transport from a significant heating that occurs upstream of the power injection point, in the absence of a concomitant electrical current. By tuning in situ the edge path, we show that the chargeless heat transport does not follow the reverse direction of the electrical current path along the edge. This unexpected heat conduction, whose mechanism remains to be elucidated, may play an important role in the physics of the fractional quantum Hall regime.