Body-centered-cubic (BCC) high entropy alloys (HEAs) can show exceptionally high strength up to high temperatures. Mechanistic theories are needed to guide alloy discovery within the immense multicomponent HEA compositional space. Here, two new theories for strengthening as controlled by screw and edge dislocations, respectively, are applied to predict the yield stresses of a range of BCC alloys over a wide range of temperatures. Results show that the screw theory, with one fitting parameter, can capture experiments in many dilute and non-dilute alloys while the parameter-free edge theory agrees with experiments in non-dilute alloys having a sufficiently large misfit parameter. These results indicate a transition in single-phase alloy strengthening from traditional screw dominance to edge dominance with increasing misfit that is enabled in complex non-dilute alloys. These results point to the use of the edge theory to guide design of high-temperature alloys in the non-dilute range.