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The purpose of this paper is to introduce a new time-fractional heat conduction model with three-phase-lags and three distinct fractional-order derivatives. We investigate the introduced model in the situation of an isotropic and homogeneous solid sphere. The exterior of the sphere is exposed to a thermal shock and a decaying heat generation rate. We recuperate some earlier thermoelasticity models as particular cases from the proposed model. Moreover, the effects of different fractional thermoelastic models and the effect of instant time on the physical variables of the medium are studied. We obtain the numerical solutions for the various physical fields using a numerical Laplace inversion technique. We represent the obtained results graphically and discuss them. Physical views presented in this article may be useful for the design of new materials, bio-heat transfer mechanisms between tissues and other scientific domains. [ABSTRACT FROM AUTHOR]