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Following up on @J.M.'s observations in the comments, differentiate $$m(t)=m(0)-\frac{T(t)-T_0}{Q_S}$$ to get $$\frac{dm}{dt}=-\frac{T'(t)}{Q_S}$$ Combine with $$\frac{dm}{dt}=4 \, T(t)^{3}+T(t)^{2}$$ to get a differential equation in T[t]: $$T'(t)=-\text{Qs} \left(4 \, T(t)^3+T(t)^2\right)$$ Use DSolve with initial value T[0] == t0: DSolve[{T'[t] ...