Helium-aided sintering of porous unsintered glass is a complex multiscale process, characterised by three different timescales, namely, that of helium diffusion, heat conduction, and radial shrinkage of the glass core This work presents a multiscale model for quantifying heat and helium diffusion in a shrinking core system by decoupling the timescales based on their orders of magnitude We obtain analytical solutions of our model, which allow us to quantify the spatio-temporal profiles of temperature and helium concentration in the glass during the sintering process Our results show that the introduction of helium increases the sintering rate of glass, and we conclude that pre-sintering heating followed by helium-aided sintering is better than simultaneous heating and helium diffusion We also show that the pre-sintering heating process for a standard glass sample should not be longer than an hour for the sake of heat economy, following which we may switch to the helium-aided sintering process, where the sintering should occur under isothermal conditions for approximately 6 h We perform dynamic simulations using glass porosity as a parameter, and find the sintering rate to be directly proportional to the initial porosity of the glass sample