In this work, we report the ab initio numerical simulation investigation on the crystal lattice, electronic structure, optical, and transport properties of pure and C‐doped crystalline hafnium dioxide (c‐HfO2) using FP‐LAPW method. Different exchange correlation functionals like generalized gradient approximation (GGA) of PBE‐sol and Tran and Blaha's modified Becke‐Johnson exchange potential (mBJ) within density functional theory have been used. Two kinds of defects in cubic pure HfO2 have been investigated: one is substitution of Hf atom by C impurity and other substitution of O atom by C impurity in crystalline HfO2. The computed results indicate that impurity energy bands as a result of 2p states of C are found to present in the band gap of c‐HfO2. Few of these bands are present at the conduction band minimum, which results to a noteworthy band gap contraction, and hence electrons close to Fermi level get transferred in doped c‐HfO2. We have also analysed the dielectric function, absorption coefficient, optical conductivity, optical function, electron energy loss, and reflectivity for both pure HfO2 and doped with C. Furthermore, the temperature‐dependent transport properties of C‐doped HfO2 are also discussed in terms of Seeback coefficient, thermal conductivities, electronic conductivities, power factor, and figure of merit in the temperature range 0 to 1200 K. The calculated value of PF for pure HfO2 was found to increase from 0.01 × 1012 WK−2m−1s−1 at 50 K to 1.79 × 1012 WK−2m−1s−1 at 1200 K and for HfO2(1 − x)Cx it was found to increase from 0.06 × 1012 WK−2m−1s−1 at 50 K to 0.25 × 1012 WK−2m−1s−1 at 1200 K.