A method and apparatus for assembling a semiconductor device. A chip (901) with solder bodies (903) on its contact pads is flipped onto a substrate (904). After the reflow process, a gap (910) spaces chip and substrate apart. A polymer precursor is selected for its viscosity of known temperature dependence. The apparatus has a plate (800) with heating and cooling means to select and control a temperature profile from location to location across the plate. After preheating, the assembly is placed on a mesa (801) of the plate configured to heat only a portion of the substrate. Movable capillaries (840, 921) blow cooled gas onto selected locations of the assembly. After the temperature profile is reached, a quantity of the precursor is deposited at a chip side and pulled into the gap by capillary action. The capillary flow is controlled by controlling the precursor viscosity based on the temperature profile, resulting in a substantially linear front, until the gap is filled substantially without voids.