How to solve heat equation with Robin type conditions with NDSolve?

Could you help me please to solve following problem! I need to solve one-dimensional heat equation with Robin type boundary conditions. But Mathematica find only constant solution with no dependence on time and space coordinates. My code:

NDSolve[{
   D[T[x, t], t] - D[D[ T[x, t], x], x] == 0,
   (D[T[x, t], x] - (T[x, t] - 100) == 0) /. x -> 0, 
   (D[T[x, t], x] + (T[x, t] - 20) == 0) /. x -> 1, 
   T[x, 0] == 20
}, T, {x, 0, 1}, {t, 0, 1}]

Mathematica returns that temperature will be constant in all region: T[x,t]=20 (but in steady state solution we will have the liner low for the T(x)).

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