Youssef improved the generalized thermoelasticity base on two distinct temperatures; the conductive temperature and the thermodynamics temperature which coincide together when the heat supply vanishes [1, 2]. This theory has one paradox, where it offers an infinite speed of thermal wave propagation. So, this work assuming a new consideration of the two types of temperature which depends upon the acceleration of the conductive and the thermal temperature. This work introduces the proof of the uniqueness of the solution, moreover, one dimensional numerical application. According to the numerical result this new model of thermoelasticity offers finite speed of thermal wave and mechanical wave propagation.