Graphene exhibits exceptional thermal conductivity, making it a promising material for thermal management applications. The thermal properties are highly anisotropic, with in-plane conductivity far exceeding out-of-plane values. This anisotropy arises from the strong covalent sp² bonding within the basal plane compared to weak van der Waals interactions between layers. Monolayer graphene demonstrates in-plane thermal conductivity ranging from 2000 to 5000 W/mK near room temperature, among the highest of any known material. In contrast, the cross-plane conductivity is orders of magnitude lower, typically below 10 W/mK. The disparity highlights the importance of phonon transport mechanisms and structural orientation in heat dissipation.

Phonons dominate thermal transport in graphene due to its lack of free electrons at the Dirac point. Three acoustic phonon modes contribute to heat conduction: longitudinal acoustic (LA), transverse acoustic (TA), and out-of-plane acoustic (ZA). The LA and TA modes exhibit linear dispersion near the Brillouin zone center, while the ZA mode shows quadratic dispersion. At room temperature, the ZA mode contributes significantly despite its lower group velocity because of its high density of states and long mean free path. Umklapp scattering becomes the primary limiting factor for high-temperature thermal conductivity, reducing phonon mean free paths and increasing resistive phonon-phonon interactions. Boundary scattering also plays a critical role in finite-sized graphene flakes or near defects, further modulating thermal transport.

Measuring graphene's thermal conductivity presents challenges due to its atomic thickness. Raman thermometry has emerged as a widely used technique, leveraging the temperature-dependent shift of the G-peak in graphene's Raman spectrum. By locally heating the sample with a laser and analyzing the spectral shifts, researchers can extract thermal conductivity values. Another approach involves microfabricated devices with integrated heaters and thermometers to directly measure heat flow across suspended graphene membranes. Time-domain thermoreflectance (TDTR) offers additional insights, particularly for cross-plane measurements in multilayer graphene or graphene-substrate systems. Each method has limitations, with Raman thermometry being sensitive to laser absorption coefficients and TDTR requiring careful calibration of transducer layers.

Substrate interactions significantly alter graphene's thermal properties. When graphene is supported on a substrate like SiO₂, the thermal conductivity can drop by a factor of two to ten compared to suspended graphene. This reduction stems from phonon leakage into the substrate, increased scattering at interface defects, and strain-induced modifications to phonon dispersion. The substrate's Debye temperature relative to graphene's also influences energy transfer efficiency. Hexagonal boron nitride (hBN) substrates generally preserve higher thermal conductivity than SiO₂ due to better lattice matching and reduced interfacial disorder. Understanding these effects is crucial for designing graphene-based thermal management solutions in real-world applications where substrate coupling is unavoidable.

In electronics thermal management, graphene's high in-plane conductivity enables efficient lateral heat spreading. Applications include heat spreaders for high-power transistors, thermal interface materials, and passive cooling films. However, practical implementation faces several limits. The primary bottleneck lies in the thermal boundary resistance between graphene and other materials, hindering efficient heat extraction from hotspots. Even with ideal graphene, the cross-plane resistance prevents effective vertical heat dissipation in multilayer stacks. Additionally, defects, grain boundaries, and edge scattering in large-area polycrystalline graphene films degrade performance compared to pristine single crystals. For device integration, the trade-off between thermal enhancement and electrical interference must also be carefully managed, though this falls outside the scope of purely thermal considerations.

Emerging approaches aim to overcome these limitations through structural engineering. Graphene laminates with aligned platelets can enhance cross-plane conductivity while maintaining high in-plane performance. Hybrid structures combining graphene with metallic nanoparticles or vertical carbon nanotubes attempt to bridge the out-of-plane heat transfer gap. Another strategy involves strain engineering, where controlled tensile strain can modify phonon dispersion relations to favor specific transport directions. However, each solution introduces new complexities, such as increased interfacial resistance or mechanical stability concerns.

The temperature dependence of graphene's thermal conductivity reveals further nuances. At cryogenic temperatures, conductivity follows a T³ trend due to the dominance of boundary scattering. Around room temperature, Umklapp processes cause conductivity to decrease with increasing temperature, typically following a 1/T relationship. Above 400 K, substrate interactions and radiative losses become increasingly significant. These trends inform operating conditions for graphene-based thermal solutions, particularly in high-power electronics where junction temperatures may exceed 100°C.

Future advancements in graphene thermal applications will likely focus on optimizing interfacial engineering and scalable manufacturing. Large-area chemical vapor deposition (CVD) graphene must improve in crystalline quality to rival exfoliated flakes in thermal performance. Advances in transfer techniques that minimize interfacial contamination will also be critical. For industrial adoption, cost-effective production of graphene with tailored thermal properties remains a key challenge. While fundamental limits exist due to phonon physics, continued progress in material synthesis and integration schemes promises to unlock graphene's full potential in next-generation thermal management systems.

The unique combination of high thermal conductivity, lightweight nature, and chemical stability positions graphene as a transformative material for heat dissipation challenges. From high-frequency electronics to aerospace systems, the ability to rapidly redistribute heat at the nanoscale could enable breakthroughs in device performance and reliability. As measurement techniques and theoretical models continue to improve, so too will the precision with which graphene's thermal properties can be harnessed for targeted applications. The ongoing exploration of defect engineering, alloying, and hybrid structures ensures that graphene will remain at the forefront of thermal materials research for years to come.