Field pennycress (Thlaspi arvense: Brassicaceae) is a winter annual currently undergoing domestication as a combined cash/cover crop. While pennycress has impressive cold tolerance, it is sensitive to heat stress, particularly during flowering. Previous efforts to improve oil quality, via CRISPR gene editing, have created lines with reduced polyunsaturated fatty acid content, through loss of function of the fatty acid desaturase (fad2) and reduced oleate desaturase (rod1) genes.  This has the potential to alter heat and cold tolerance, as colder climates are often associated with greater lipid unsaturation. In several growth chamber experiments, we explored tolerance to heat stress during flowering in pennycress lineswith loss of function of either rod1 and fad2.  Seed yield, lipid peroxidation (as an index of stress), and pollen viability at a series of temperatures were measured. We also conducted a study of heat stress tolerance, including pollen viability and photosynthetic assimilation under heat stress, in natural  accessions selected from the northern and southern limits of their North American range. Both fad2 and rod1 lines had increased pollen viability (70% and 50% respectively) under moderate heat stress (28 °C) compared to their wild type parent (30%). They also showed smaller increases in lipid peroxidation, and smaller decreases in seed yield, following a 9 day treatment at 34 °C. . Southern accessions showed greater pollen viability at high temperatures than northern lines (e.g. 35% viability at 34 °C compared to 6%). Southern accessions also retained more of their photosynthetic capacity at 34 °C compared to northern lines. Our ongoing efforts serve as a starting point for improving heat stress in pennycress, both through gene editing and identification of natural variation, and rendering this emerging crop more resilient to global warming.