Glass is among the most common materials in our everyday lives. And yet the science behind this interesting, complex and ubiquitous material is seldom considered in the undergraduate science curriculum. The glass transition (Tg) is both a fundamental and defining concept in understanding the glassy state. To facilitate the experimental exploration of this important topic we have developed a simple home-built apparatus for measuring the Tg and the associated relaxation phenomena. The simple differential thermal analysis (DTA) apparatus requires only basic mechanical and electronic construction skills yet provides excellent resolution of the Tg for the low temperature sugar glasses examined. We also demonstrate the strong effect of thermal history on Tg, including both the effect of cooling rate and aging. This apparatus provides an interesting and intuitive path to the student's exploration and understanding of the glassy state and provides a resource for deeper, independent and open-ended study of the relaxation phenomena, especially appropriate for an advanced undergraduate laboratory.