When you do read the Schwartz paper, look for the detrending of long time series. He admits that the climate does respond at different rates depending on the mechanism associated with the forcing, so why the bias towards shorter time periods by removing longer trends?
My guess would be that it is easier to distinguish short term signals from noise then it is to distinguish long term signals from noise. Clearly the temperature at the bottom of the ocean is going to respond much slower then the temperature near the surface of the ocean. As a consequence the low the frequency of the driving signal the greater the effective heat heat capacity.
Also as far as nonlinearities go the larger the signal, the greater the effective heat capacity. Consequently the sensitivity of climate to CO2 should depend both on the frequency and amplitude of the signal.