A thermal profile has been measured in a 1000 m deep borehole intersecting the active Aigio fault, Corinth Rift, Greece. The heat flow is 53 mW/m2, indicating that the rifting process has no effect in heat flow. The temperature near the fault is higher than expected from a pure conductive model. This discrepancy is not due to fluid flow above the fault as shown by the long term monitoring of downhole pressure. Neither can it be attributed to the fault slip since the Aigio fault is a minor normal fault of the rift, with no very recent earthquake. We propose that the anomaly is due to the convection within the karst that constitutes the footwall. Numerical simulations give a correct estimate for the recorded temperature increase. This is an extreme case of thermal disturbance induced near a fault by local fluid circulation. The occurrence of convection outside geothermal area is very rare.