The paper studies the wetting of grain boundary triple junctions (GB TJs) by the second solid phase (intermetallic) delta in the Cu-In alloys. In this system, the portion of grain boundaries in a copper-based solid solution (Cu), which are "wetted" by the second solid phase delta, changes non-monotonically with increasing temperature. At first, the portion of such completely wetted GBs increases from zero to almost 100% when the sample is heated, and then quickly falls back to zero. The condition of complete wetting for the GB TJs (sigma(GB) > 1.73 sigma(SS)) is less stringent than for the GBs (sigma(GB) > 2 sigma(SS)). Therefore, if the transition from incomplete to complete wetting occurs with an increase in temperature, then all GB TJs should become completely wetted at a temperature T-WTJ, lower than the temperature T-WGB, at which all GBs become completely wetted. In this work on the Cu-In system, it was found experimentally for the first time that the wetting of the GB TJs also behaves non-monotonously. The percentage of wetted GB TJs also increases to 100% at first and then falls with increasing temperature. In this case, the portion of wetted GB TJs exceeds the portion of wetted GBs not only when it increases with increasing temperature, but also then, with the subsequent disappearance of fully wetted GBs.