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In this work, we resolved some controversial issues on theBloch-Gr\"{u}neisen (BG) temperature in doped graphene via analytical andnumerical calculations based on full inelastic electron-acoustic-phonon (EAP)scattering rate and various approximation schemes. Analytic results for BGtemperature obtained by semi-inelastic (SI) approximation (which givesscattering rates in excellent agreement with the full inelastic scatteringrates) are compared with those obtained by quasi-elastic (QE) approximation andthe commonly adopted value of $\Theta^{LA}_{F} = 2\hbar v_{LA} k_F/k_B$. It isfound that the commonly adopted BG temperature in graphene ($\Theta^{LA}_{F}$)is about 5 times larger than the value obtained by the QE approximation andabout 2.5 times larger than that by the SI approximation, when using thecrossing-point temperature where low-temperature and high-temperature limits ofthe resistivity meet. The corrected analytic relation based on SI approximationagrees extremely well with the transition temperatures determined by fittingthe the low- and high-$T$ behavior of available experimental data of graphene'sresistivity. We also introduce a way to determine the BG temperature includingthe full inelastic EAP scattering rate and the deviation of electron energyfrom the chemical potential ($\mu$) numerically by finding the maximum of$\partial \rho(\mu,T)/\partial T$. Using the analytic expression of$\Theta_{BG,1}$ we can prove that the normalized resistivity defined as$R_{1}=\rho(\mu,T)/\rho(\mu,\Theta_{BG,1})$ plotted as a function of$(T/\Theta_{BG,1})$ is independent of the carrier density. Applying our resultsto previous experimental data extracted shows a universal scaling behavior,which is different from previous studies.

Bloch-Gr\"{u}neisen temperature and universal scaling of normalized resistivity in doped graphene revisited