Quantum reactive calculations are presented for an ion-atom reaction involving the HeH(+)cation and its destruction via a barrierless interaction with H atoms. The range of collision energies considered is that of a cold trap regime (around and below millikelvin) where the ionic partner could be spatially confined. Specific resonant features caused by the interplay of the strong ionic interaction with the very slow partners' dynamics are found and analyzed. Indications are also given on the consequences of the abstraction mechanism that acts for this reaction at low energies.