This paper presents an original systematic experimental investigation of the transient transport phenomena occurring during the pile-up of molten, picoliter-size liquid metal droplets. The prevailing physical mechanisms of the pile up process are identified and quantified experimentally. In terms of relevant dimensionless groups the following ranges are covered: Re = 281-453, We = 2.39-5.99, Ste = 0.187-0.895. This corresponds to molten solder droplets impinging at velocities ranging between 1.12 and 1.74 m/s having an average diameter of 78 mum. The impact fluid dynamics, cooling and subsequent solidification of the second (top) droplet in the pile-up is strongly influenced by the geometry of the first, already solidified droplet, upon which it impinges. The solidification time depends, in addition to the thermal contact resistances at the interfaces, on the transport of heat through the solid structures above the flat wafer substrate. The total solidification time of the second droplet depends non-monotonically on the substrate temperature, initially increasing with decreasing substrate temperature. The impact velocities affect strongly the final shapes of the observed pile up structures. For decreasing Stefan number (i.e. higher substrate temperature) an increasing importance of wetting phenomena is observed.