The correct choice is (a) (frac{T(t+Delta t)-T(t-Delta t)}{2 Delta t})
To explain: The Crank-Nicolson scheme uses the previous and the next steps to get the derivative at the current step. Expressing it mathematically,
(frac{partial T(t)}{partial t} = frac{T(t+Delta t)-T(t-Delta t)}{2 Delta t}).