One of the hallmarks of a living cell is that it can duplicate itself. An important question is when and why a cell might permanently lose its ability to self-replicate (lose viability) and thereby transition into being a dead cell. In this talk, I will describe two studies in which we used the budding yeast, S. cerevisiae, and modeling to answer these questions in the context of high and frigid temperatures. Temperature is a universal parameter for living systems in that it controls the speed of all biochemical reactions in all organisms and every habitat. By either increasing the temperature to sufficiently high values or decreasing the temperature to sufficiently low values, we aimed to drastically slow down the pace at which yeast’s replicative life could proceed. By doing so, we uncovered principles that limit self-replication at high and near-freezing temperatures. For both high temperatures (> 38 C) and near-freezing temperatures (0 C - 5 C), we found ways to extend yeast's ability to duplicate: we could enable more cells to duplicate with drastically shortened doubling times. We constructed "phase diagrams" that describe cell-population growths for both temperature regimes. The same mathematical model, with one free parameter, reproduced both phase diagrams as well as stochastic proliferation of individual cells. At near-freezing temperatures, we discovered "speed limits” for yeast: the smallest and largest possible cell-doubling times defined for each frigid temperature. A cell that progresses more slowly than a "low-speed limit" defined for each temperature faces a certain death. A mathematical model and experimental data elucidated how these speed limits arise and fundamental barriers to thermally slowing down the self-replication dynamics of a cell.