This thesis constitutes an investigation into student understanding of concepts in thermal physics in an introductory calculus-based university physics course. Nearly 90% of students enrolled in the course had previous exposure to thermodynamics concepts in chemistry and/or high-school physics courses. The two major thrusts of this work are (1) an exploration of student approaches to solving calorimetry problems involving two substances with differing specific heats, and (2) a careful probing of student ideas regarding certain aspects of entropy and the second law of thermodynamics. We present extensive free-response, interview, and multiple-choice data regarding students' ideas, collected both before and after instruction from a diverse set of course semesters and instructors. For topics in calorimetry, we found via interviews that students frequently get confused by, or tend to overlook, the detailed proportional reasoning or algebraic procedures that could lead to correct solutions. Instead, students often proceed with semi-intuitive reasoning that at times may be productive, but more often leads to inconsistencies and non-uniform conceptual understanding. Our investigation of student thinking regarding entropy suggests that prior to instruction, students have consistent and distinct patterns of incorrect or incomplete responses that often persist despite deliberate and focused efforts by the instructor. With modified instruction based on research-based materials, significant learning gains were observed on certain key concepts, e.g., that the entropy of the universe increases for all non-ideal processes. The methodology for our work is described, the data are discussed and analyzed, and a description is given of goals for future work in this area.