This measured soil temperature profile seem strange to me. We know from heat equation that heat transfers at infinite speed in media so if there's a boundary change in temperature, any interior point in the media will have temperature change simultaneously. This picture apparently says that when 0m has temperature jump, there's no response at 0.1m below surface. Isn't it wrong?
The picture shows the change of temperature at different depth when a prescribed temperature signal is applied at one boundary. The other boundary (~1m) is kept at a constant temperature. With a few assumptions it is a valid application of the heat equation.
Following Fourier's law we have a heat flux (energy per unit time and unit area) that is proportional to the temperature gradient: $q = k \times \frac{{d T}}{{d x}}$ (in one dimension). With q the heat flux, T the temperature, x the position (i.e. the depth in the soil) and k the conductivity (W/(m·K)).
So the change is not instantaneous but depends on the temperature difference and also the properties of your medium: with high k, the temperatures propagates faster to the lower layers, but the medium density and heat capacity will also come into account.