A melt extrusion-based 3D printing technique has been employed to fabricate a microcapillary electroosmotic pump (EOP) structure from a medical grade polyurethane (PU) elastomer in combination with a thermally conductive boron nitride (BN) nanopowder as a heat dissipating component at loadings of 0, 1, 3, 5, 10 and 20% w/w. Using a negative space 3D printing technique, a longitudinal body-centre cubic (BCC) log-pile like filament arrangement was used to fabricate functional capillary structures. These 3D printed capillaries were shown to function as simple electroosmotic pumps achieving flow rates of 1.2 µl/min at applied electric fields up to 750 V/cm. A limitation of the EOP design is the internal production of heat at higher operational voltages due to Joule heating effects which results in a non-linear flow behaviour. BN loadings up to 20% w/w were shown to reduce the operational temperature of the PU EOP by 20°C.