A first substrate mounted to a bonder head and a second substrate mounted to a base plate are held at different elevated temperatures at the time of bonding that provide a substantially matched thermal expansion between the second substrate and the first substrate relative to room temperature. Further, the temperature of the solder material portions and the second substrate is raised at least up to the melting temperature after contact. The distance between the first substrate and the second substrate can be modulated to enhance the integrity of solder joints. Once the distance is at an optimum, the bonder head is detached, and the bonded structure is allowed to cool to form a bonded flip chip structure. Alternately, the bonder head can control the cooling rate of solder joints by being attached to the chip during cooling step.