The fractional conformable derivative and its properties have been introduced recently. Using this derivative we obtain a new class of smooth solutions for the Newton’s law of cooling in terms of a stretched exponential function depending on the fractional order parameter 0 < γ ≤ 1. In addition, the convection coefficient of fractional order k(γ) can be calculated easily. Also, it is shown, that in the particular case γ = 1 these solutions become the ordi- nary ones.