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 x 10(12) WK(-2)m(-1)s(-1) at 50 K to 1.79 x 10(12) WK(-2)m(-1)s(-1) at 1200 K and for HfO2(1 - x)Cx it was found to increase from 0.06 x 10(12) WK(-2)m(-1)s(-1) at 50 K to 0.25 x 10(12) WK(-2)m(-1)s(-1) at 1200 K.