We have used a higher-order fluid model to study the effect of time-dependent coronal heating of protons on the solar wind, both for the fast wind from rapidly expanding coronal holes and for slower winds from a radially expanding geometry. The model extends from the chromosphere to 1 AU in order to capture the coupling between the chromosphere and corona and therefore the supply of plasma to the solar wind. The protons are heated in the perpendicular direction (relative to the magnetic field), assuming a simple sinusoidal variation with time. With a short time period for the heating, less than about 3 hours, the oscillations are efficiently damped in the inner part of the solar wind, even when the amplitude of the change in heating rate is large, leading to essentially steady state solutions near Earth. Heating with a period of 10 hours or so leads to perturbations in the wind near Earth that are comparable to Ulysses observations. Heating with a period of order 100 hours leads to essentially a series of steady state solutions. The mass flux perturbations are in general larger than the perturbations in wind speed, and for heating of coronal holes with periods of order 30 hours the mass flux perturbations are amplified in the wind by the interaction between the fast and slow components of the wind. In this case even moderate changes in the heating rate in the corona can produce solar wind interaction regions with forward and reversed shocks and large mass flux perturbations near Earth.