Thermopower (TP), S of pure graphene in the Bloch–Grüneisen (BG) regime is investigated assuming electrons to be scattered by in-plane acoustic phonons and taking into account the temperature dependent effects arising from thermal averaging over carrier energy. Numerical calculations of electron mobility and TP show a signature of BG regime. The mobility is found to increase rapidly with decrease in temperature. The diffusion component Sd of TP is found to follow a non-linear temperature dependence showing changes in sign before becoming linear at very low temperatures; this is in contrast to the usual linear dependence reported in literature. At higher temperatures Sd, as does mobility, is found to merge with values calculated using equipartition approximation. The influence of phonon drag contribution Sg on the total TP, S, is also investigated. A fairly good agreement with existing low temperature data is obtained. Detailed analysis of TP data in pure samples will enable better understanding of the electron–phonon interaction in graphene.