The process of composite metal foil manufacturing (CMFM) has reduced a number of limitations associated with commercial additive manufacturing (AM) methods. The existing metal AM machines are restricted by their build envelope and there is a growing market for the manufacture of large parts using AM. These parts are subsequently manufactured in fragments and are fastened together. This paper analyses the thermal stresses around cylindrical fasteners for three layered metal composite parts consisting of aluminium foil, brazing paste and copper foil layers. The investigation aims to examine the mechanical integrity of the metallurgically bonded aluminium/copper foils of 100 micron thickness manufactured in a disc shape. A cylindrical fastener set at an elevated temperature of 100 °C is fitted in the middle of the disc which results in a steady-state thermal distribution. Radial and shear stresses are computed using finite element method which shows that non-zero shear stresses developed by the copper layer inhibit the axial slippage of the fastener and thereby establishing the suitability of rivet joints for CMFM parts.