In this work we conduct a transient heat conduction experiment with an aqueous suspension of nanoparticle disks of Laponite JS, a sol forming grade, using laser light interferometry. The image sequence in time is used to measure the thermal diffusivity and thermal conductivity of the suspension. Imaging of the temperature distribution is facilitated by the dependence of the refractive index of the suspension on temperature itself. We observe that with the addition of 4 vol % nanodisks in water, the thermal conductivity of the suspension increases by around 30%. A theoretical model for the thermal conductivity of the suspension of anisotropic particles by Fricke as well as by Hamilton and Crosser explains the trend of data well. In turn, it estimates the thermal conductivity of the Laponite nanoparticle itself, which is otherwise difficult to measure in a direct manner. We also measure the viscosity of the nanoparticle suspension using a concentric cylinder rheometer. Measurements are seen to follow quite well the theoretical relation for the viscosity of suspensions of oblate particles that includes up to two-particle interaction. This result rules out the presence of clusters of particles in the suspension. The effective viscosity and thermal diffusivity data show that the shape of the particle has a role in determining the enhancement of thermophysical properties of the suspension.