Concentrator photovoltaic (CPV) systems replace semiconductor material by cost-efficient optical elements. The potential cost reduction of these systems is closely related to the concentration factor because higher light concentrations imply lower amount of semiconductor material required for the solar cells. Thus, one promising way for improving this technology is moving towards ultra-high (UH) concentration levels (> 2000 suns). However, the thermal management at such extreme light fluxes is difficult. Using small-sized solar cells is beneficial for improving the thermal management. Among the possible cooling strategies, the use of flat-plate heat-sinks for passive cooling, if feasible, would be the simplest way to dissipate the heat and would accelerate the development of UHCPV prototypes. However, the feasibility of flat-plate heat-sinks using microscale solar cells for UHCPV applications has not been analysed in detail yet. In this work, a thermal 3D finite-element model is used to investigate the possibilities of flat-plate heat-sinks at concentration ratios not tested to date, i.e. 2000-10,000 suns. Critical parameters such as solar cell area and efficiency, substrate thickness, heat-sink area, and heat-sink material are evaluated and discussed. Results show that solar cells of 1 mm x 1 mm area or below can be thermally handled with conventional Aluminium flat heat-sinks up to 10,000 suns.