We demonstrate optically tunable control of second-harmonic generation in all-dielectric nanoantennas: by using a control beam that is absorbed by the nanoresonator, we thermo-optically change the refractive index of the radiating element to modulate the amplitude of the second-harmonic signal. For a moderate temperature increase of roughly 40 K, modulation of the efficiency up to 60% is demonstrated; this large tunability of the single meta-atom response paves the way to exciting avenues for reconfigurable homogeneous and heterogeneous metasurfaces.