17 pages, 3 Postscript figures, latex.We couple fermion fields in the adjoint representation (gluinos) to the SU(2) gauge field of unit charge calorons defined on R^3 x S_1. We compute corresponding zero-modes of the Dirac equation. These are relevant in semiclassical studies of N=1 Super-symmetric Yang-Mills theory. Our formulas, show that, up to a term proportional to the vector potential, the modes can be constructed by different linear combinations of two contributions adding up to the total caloron field strength.We acknowledge financial support from the Comunidad Autónoma de Madrid under the program PRICyT-CM-5 S-0505/ESP-0346. M.G.P. acknowledges financial support from a Ramón y Cajal contract of the MEC. M.G.P. is partially supported by the Spanish DGI under contracts FPA2003-03801 and FPA2003-02877. A.G-A is partially supported by the Spanish DGI under contracts FPA2003-03801 and FPA2003-04597.