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The stable and efficient operation of the transmission network is fundamental to the power system's ability to deliver electricity reliably and cheaply. As average temperatures continue to rise, the ability of the transmission network to meet demand is diminished. Higher temperatures lead to congestion by reducing thermal limits of lines while simultaneously reducing generation potential. Due to prohibitive costs and limited real estate for building new lines, it is necessary to consider capacity expansion as well to improve the functioning and efficiency of the grid. Optimal control, however, requires many discrete choices, rendering fully accurate models intractable. Furthermore, temperature changes will impact different regions and climate differently. As such, it is necessary to model both temperature changes and transmission flows with high spatial resolution. This work proposes a case study of the transmission grid centered in Arizona, using a DC optimal power flow mathematical formulation to plan for future transmission expansion and capacity expansion to efficiently meet demand. The effects of rising temperatures on transmission and generation are modeled at the regional level. Several classes of valid inequalities are employed to speed up the solution process. Multiple experiments considering different temperature and demand trends are considered which include each of the above technologies.

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