The direct observation of space charge injection, transport, accumulation, and recombination in solid dielectrics, as well as their spatial evolution over time, is of considerable importance in the investigation of design stress and the aging mechanism of engineering dielectrics under a high electric field. In a high-voltage direct current (HVDC) power cable with an expected temperature gradient at operating temperature and electric field, the spatial variation of the ratio of two electromagnetic constitutive parameters of the cable dielectric, the permittivity vs conductivity, acquires the presence of space charge across the insulation. Such a space charge distribution depends strongly on the temperature and electric field coefficients of these electromagnetic constitutive parameters. In addition, the injection of charges across the conductor/insulation interface and the subsequent transport, trapping and detrapping of these charges over various chemical and physical defects further enhance the electric field distortion and aging of cable dielectrics. Numerous studies have been conducted under a parallel-plate configuration to understand such a space charge effect. However, nearly all of them were conducted under uniform isothermal conditions. The ability to perform a space charge profiling study under a thermal gradient in the development phase of new extruded high-voltage direct current cable materials brings in the most value upstream. In this study, through model-aided design, a parallel-plate, pulsed-electroacoustic (PEA) space charge profiling technique is extended to include a thermal gradient in flat dielectric samples. The space charge behavior and dynamics within flat dielectric specimens in the presence of a thermal gradient have been studied extensively through a modified PEA system to provide insights into the high-field aging mechanisms of new materials developed for energy-efficient power devices and renewable integration.