Laser physical vapor deposition is used to deposit thin films of lithium phosphorous oxynitride in nitrogen and lithium nickel manganese oxide in oxygen ambient on Si substrate. LIPON film is also deposited on LiNiMnO film that is deposited on Si. Graphene films consisting of graphene platelets are deposited on Si substrate from a suspension in isopropyl alcohol. Li-graphene films are obtained after Li adsorption by immersion in LiCl solution and further drying. Transient thermo reflectance signal is used to determine the cross-plane thermal conductivity of different layers and interface thermal conductance of the interfaces. The results show that LIPON film with lower thermal conductivity is a thermal barrier. The interface thermal conductance between LIPON and Au or Si is found to be very low. Thermal conductivity of LiNiMnO is found to be reasonably high so that it is not a barrier to thermal transport. Film with graphene platelets shows a higher value and Li adsorbed graphene film shows a much higher value of cross-plane thermal conductivity. The value of interface thermal conductance between graphene and Au or Si (100) substrate is also much lower. The implications of the results for the thermal transport in thin film Li batteries are discussed.