Charge mobility, a pivotal parameter in the space charge analysis model for oil-pressboard insulation of converter transformer under DC electric fields, predominantly relies on theoretical or empirical data. The prevalent omission of empirical, measurement-based evaluations, combined with the neglect of temperature and electric field intensity effects, introduces uncertainties in the calculation of electric field and charge dynamics. Grounded on the principles of the electroacoustic pulse technique for space charge measurements, our investigation established a temperature-controlled platform to determine the charge-charge mobility in oil and pressboard insulation mediums. Utilizing diverse oil-pressboard insulation systems, this study identified the temporal patterns of both positive and negative charge mobilities and unravelled the mechanisms modulated by temperature and electric field intensity: 1) With increasing temperatures (from 20°C to 80°C) and intensifying electric field strengths (from 5kV/mm to 25kV/mm), the charge mobility within transformer oil and pressboard exhibits a rising trend. Notably, temperature variations exert the most significant influence, yielding amplifications up to 24.8 times. 2) The intrinsic properties of different transformer oils and oil-impregnated pressboards result in pronounced differences in their charge transport behaviours. Specifically, naphthenic-based oil demonstrates enhanced charge mobility relative to its paraffin-based counterpart. In contrast, transformer oils with higher kinematic viscosities exhibit diminished charge mobility compared to those with lower viscosities. 3) A linear relationship is observed between the oil absorption rate and electrical conductivity, aligning closely with the insulating pressboard's charge mobility. The evaluation of electric field and interface charge dynamics in oil-pressboard insulation under both DC and polarity-reversed conditions revealed that the electric field decay in naphthenic-based oil is more rapid than in paraffin-based oils. Moreover, both the magnitude and rate of interface charge accumulation in naphthenic-based oils exceed those in paraffin-based variants, further validating the accuracy of our charge mobility measurements and ensuing analysis.