In this study, we investigate the temperature- and temperature gradient-dependent magnetization reversal process of individual, single-domain Co39Ni61 and Fe15Ni85 ferromagnetic nanowires via the magneto-optical Kerr effect and magnetoresistance measurements. While the coercive fields (H-C) and therefore the magnetic switching fields (H-SW) generally decrease under isothermal conditions at elevated base temperatures (T-base), temperature gradients (Delta T) along the nanowires lead to an increased switching field of up to 15\% for Delta T = 300 K in Co39Ni61 nanowires. This enhancement is attributed to a stress-induced, magneto-elastic anisotropy term due to an applied temperature gradient along the nanowire that counteracts the thermally assisted magnetization reversal process. Our results demonstrate that a careful distinction between locally elevated temperatures and temperature gradients has to be made in future heat-assisted magnetic recording devices.