Burn injuries are a recognized hazard in our everyday interactions with consumer products and consumer electronics. They can be painful and life-altering and can cause permanent physical as well as emotional harm. Our increasing intimacy with consumer electronics including wearables is challenging the current regulatory standard framework. The typical thermal exposure associated with wearables and consumer electronics is characterized by long duration and relatively low temperatures with a contacting object with low thermal mass. As a result, the temperature of the object changes over time and is heavily affected by the transfer of energy to the skin during contact. The current regulatory standards dealing with contact burn injury thresholds assume that the thermal energy contained within the hot object is infinite and that its surface temperature remains approximately constant during contact. This paper presents a comprehensive approach to account for the common scenario where the user contacts a finite thermal mass object. The methodology numerically solves the transient heat transfer equation in living tissues and identifies the burn injury threshold conditions associated with finite thermal mass objects. The model is able to predict burn injury by employing a concept of cumulative equivalent exposure. The predictive capabilities are validated with experimental observations of human burn injuries. This paper is the first 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. In Part II: The influence of object shape, size, contact resistance, and applied heat flux, the framework presented here in Part I is extended to investigate the effects of various contacting object conditions.