Recent high-resolution studies of the electron plasma line show that the difference between the upshifted and the downshifted frequency does not depend only on the electron drift in the plasma and on the electron temperature through the classical dispersion relation using the Maxwellian electron distribution. The difference contains an additional strong nonlinear dependence on the electron temperature. We show here that the origin of this shift in the center frequency between the upshifted and downshifted lines can easily be due to heat flows in the electron gas. We present a new expression for the dispersion relation that includes the heat flow contribution, and we use a recently acquired data set to demonstrate that the heat flow correction produces the right kind of results. For radar frequencies around 1000 MHz and plasma frequencies of the order of 7 MHz, this means that an electron temperature gradient of the order of 1 K/km can produce a difference approaching 500 Hz between the upshifted and downshifted frequencies. This shift in frequency is important, as it is comparable to the shift caused by parallel currents of a few microamperes per square meter.