The random-phase-approximation (RPA) dynamical response of liquid 3 He at finite temperatures has been calculated using an effective density-dependent atom-atom interaction. The interaction contains a zero-range part of Skyrme type, supplemented by a weighted density approximation to account for short-range correlations, and a long-range effective interaction of Lennard-Jones type. The calculated zero-sound and paramagnon energy centroids agree reasonably with data, and the calculated strength exhibits a negative energy tail extending up to -0.5 meV, also in good agreement with existing data. We have found that opposite to what happens with zero sound, within RPA the paramagnon peak is rather insensitive to thermal broadening.