Optically-transparent solids have a significant role in many emerging topics of fundamental and applied research, in areas related to Applied Optics and Photonics. In the functional devices based on them, the presence of ‘time-varying temperature fields’ critically limit their achievable performance, when used particularly for high power laser-related tasks such as light-generation, light-amplification, nonlinear-harmonic conversion etc. For optimization of these devices, accurate knowledge of the material thermal parameters is essential. Many optical and non-optical methods are currently in use, for the reliable estimation of the thermal parameters. The thermal diffusivity is a key parameter for dealing with ‘transient heat transport’ related problems. Although its importance in practical design for thermal management is well understood, its physical meaning however continues to be esoteric. The present effort concerns with a few investigations on the “Optical interrogation of ‘transient thermal conduction’ in dielectric solids”. In dielectric solids, the current understanding is that the conductive heat transport occurs only through phonons relevant to microscopic lattice vibrations. Introducing for the first time, a virtual linear translator motion as the basis for heat conduction in dielectric materials, the present investigation discusses an alternative physical mechanism and a new analytical model for the transient heat conduction in dielectric solids. The model brings into limelight a ‘new law of motion’ and a ‘new quantity’ which can be defined at every point in the material, through which time-varying heat flows resulting in time-varying temperature. Physically, this quantity is a measure for the linear translatory motion resulting from transient heat conduction. For step-temperature excitation it bears a simple algebraic relation to the thermal diffusivity of the material. This relationship helps to define the thermal diffusivity of a dielectric solid as the “translatory motion speed” measured at unit distance from the heat source. A novel two-beam interferometric technique is proposed and corroborated the proposed concept with significant advantages. Two new approaches are introduced to estimate thermal diffusivity of optically transparent dielectric solid; first of them involves measurement of the position dependent velocity of isothermal surface and second one depend on the measurement of position dependent instantaneous velocity of normalized moving intensity points. A ‘new mechanism’ is proposed and demonstrated to visualize, monitor and interrogate optically, the ‘linear translatory motion’ resulting from the transient heat flow due to step- temperature excitation. Two new approaches are introduced, first one is ‘mark’ and ‘track’ approach, it involves a new interaction between sample supporting unsteady heat flow with its ambient and produces optical mark. Thermal diffusivity is estimated by tracking the optical mark. Second one involves measurement of instantaneous velocity of optical mark for different step-temperature at a fixed location to estimate thermal diffusivity. A new inverse method is proposed to estimate thermal diffusivity and thermal conductivity from the volumetric specific heat capacity alone through thought experiment. A new method is proposed to predict volumetric specific heat capacity more accurately from thermal diffusivity.