Inside all smart devices, such as smartphones or smartwatches, there are thermally sensitive resistors known as thermistors which are used to monitor the temperature of the device. These thermistors are sensitive to temperature changes near their location on-device. While they are designed to measure the temperature of the device components such as the battery, they can also sense changes in the temperature of the ambient environment or thermal entities in contact with the device. We have developed a model to estimate core body temperature from signals sensed by these thermistors during a user interaction in which the user places the capacitive touchscreen of a smart device against a thermal site on their body such as their forehead. During the interaction, the device logs the temperature sensed by the thermistors as well as the raw capacitance seen by the touch screen to capture features describing the rate of heat transfer from the body to the device and device-to-skin contact respectively. These temperature and contact features are then used to model the rate of heat transferred from the user's body to the device and thus core-body temperature of the user for ubiquitous and accessible fever monitoring using only a smart device. We validate this system in a lab environment on a simulated skin-like heat source with a temperature estimate mean absolute error of 0.743$^{\circ}$F (roughly 0.4$^{\circ}$C) and limit of agreement of $\pm2.374^{\circ}$F (roughly 1.3$^{\circ}$C) which is comparable to some off-the-shelf peripheral and tympanic thermometers. We found a Pearson's correlation $R^2$ of 0.837 between ground truth temperature and temperature estimated by our system. We also deploy this system in an ongoing clinical study on a population of 7 participants in a clinical environment to show the similarity between simulated and clinical trials.