In this paper, theoretical investigation is performed on two-dimensional transient heat conduction in multiwall carbon nanotubes (MWCNTs) by using a continuum model. Temperature, size and direction dependencies of thermal properties are considered. Both Fourier and non-Fourier heat conduction approaches are used and finite element models are developed to solve the nonlinear equations for MWCNTs. The presented solutions are verified by comparing the results with those reported in the literature. Three types of thick and thin MWCNTs are considered and thermal shock is applied to their cylindrical surfaces or end cross sectional areas. Temperature distributions resulted from both approaches are obtained and compared together. Interesting results are found especially in MWCNTs that are exposed to extreme temperature gradient.