The shape of the electron velocity distribution function plays an important role in the dynamics of the solar wind acceleration. Electrons are normally modeled with three components, the core, the halo, and the strahl. We investigate how well the fast strahl electrons in the inner heliosphere preserve the information about the coronal electron temperature at their origin. We analyzed the data obtained by two missions, Helios, spanning the distances between 65 and 215 R S, and Parker Solar Probe (PSP), reaching down to 35 R S during its first two orbits around the Sun. The electron strahl was characterized with two parameters: pitch-angle width (PAW) and the strahl parallel temperature (T s∥). PSP observations confirm the already reported dependence of strahl PAW on core parallel plasma beta (${\beta }_{\mathrm{ec}\parallel }$). Most of the strahl measured by PSP appear narrow with PAW reaching down to 30°. The portion of the strahl velocity distribution function aligned with the magnetic field is for the measured energy range well described by a Maxwellian distribution function. T s∥ was found to be anticorrelated with the solar wind velocity and independent of radial distance. These observations imply that T s∥ carries the information about the coronal electron temperature. The obtained values are in agreement with coronal temperatures measured using spectroscopy, and the inferred solar wind source regions during the first orbit of PSP agree with the predictions using a PFSS model.