<p>This work has examined the thermal conductivity of pristine Graphene and hydrogen-, methyl-, and ethyl-functionalized Graphene over functionalization levels from 5 to 30% under tensile and compressive strains from 0 to 7%. The thermal conductivity of pristine Graphene has been reported as high as 165.71 W/m·K due to the perfect lattice structure and negligible phonon scattering, while in functionalized graphene, conductivity has been drastically reduced; the effect depends on the type and concentration of the functional group. Graphene-CH₃ has been found to present the sharpest decrease, up to 97% at 30%, and thus is highly promising for thermal insulation applications. While Graphene-H exhibited a moderate degradation, Graphene-C₂H₅ exhibited a Significant drop due to the bulkier nature of the ethyl groups. At tensile strain, for example, pristine Graphene is able to retain 74% of its conductivity at 70% strain, depicting much better resistance to deformation against its functionalized counterparts. Among the functionalized samples, Graphene-CH₃ has maintained better performance at lower strains, while Graphene-H and Graphene-C₂H₅ have shown Significant degradation beyond 5% strain. Further, compressive strain has accentuated phonon scattering with Graphene-CH₃ reaching a minimum conductivity of 0.43 W/m·K at 7% strain. These findings pointed to the chemical functionalization and tunability of graphene by mechanical strain, while the most optimal performance in high thermal conduction electronics cooling remains unmodified graphene. Above all, functionalized graphene has received promising potential in thermal insulation, especially Graphene-CH₃. It has provided critical insight into the interplay of functionalization-strain-thermal transport in graphene, thus opening up avenues for future research toward optimized functionalization methods and diversified functional groups and strain conditions.</p>