The solution of this differential equation, by integration from the initial condition, is Δ Δ T ( t ) = Δ Δ T ( 0 ) e − − t / τ τ . where Δ Δ T ( 0 ) is the temperature difference at time 0. Reverting to temperature, the solution is T ( t ) = T env + ( T ( 0 ) − − T env ) e − − t / τ τ .