Increasing use of consumer electronics such as wearables brings new concerns associated with long duration, low temperature skin burn risk. Contact with these devices of low thermal mass results in the temperature of the device changing as energy is transferred from the device to the skin during contact. Current regulatory standards concerned with contact burn injury thresholds are designed assuming that the thermal energy in the hot contacting device is infinite and that the temperature of the object does not change significantly during contact. Furthermore, geometrical aspects of the contacting objects (i.e. contact shape, object size) and operational aspects (i.e. presence or absence of heat source associated with active components) are not accounted for in the standards. This paper is the second of a two-part series that discusses a numerical methodology that relies on the concept of cumulative equivalent exposure to evaluate contact burn injury thresholds. Part I described a burn injury model which numerically solves the transient heat transfer equation in living tissues and presents the burn injury threshold conditions associated with finite thermal mass objects. In Part I, the effect of a finite thermal mass is analyzed for an infinite plate of several finite thicknesses. In Part II, the sensitivities to object shape, size, thickness, contact resistance and applied heat flux are considered.