What you are referring to are physisorption and chemisorption. They are differentiated mostly by the strength of the interaction between the sorbent and the sorbate. Skip to the highlighted text at the bottom for the punchline; otherwise, read on.
My Master's thesis - Desorption of High Explosives from Soil: Thermodynamics and the Role of Soil Organic Carbon (Minehardt, T. J, The University of Texas at Austin, August 1995) - was, until now, happily residing in a dusty part of my bookshelf, unopened for decades. Alas, it has not been digitized, and I cannot find it on the Internet (although at least one person has cited the DOE report that arose from the work I did), but there are nuggets of knowledge contained therein which I now impart to you and the masses.
First, I'll answer your question: you can, as I did, do experiments with solid-liquid mixtures at multiple temperatures and, from there, extract the enthalpies of adsorption and desorption. You need to fit data to isotherm models (Langmuir, Freundlich, linear, and BET, for example), find the best fit, and various parameters are then available to you. From these quantities, you will be able to determine the nature of the sorption interaction. Note that the best-fit isotherm type also is indicative of the type of interaction.
As for your queries about chemical sorption taking place at all temperatures, I would say that it takes place over a range of temperatures dictated by the system in question; similarly for the trend in chemical sorption - it depends. You can say, however, that physisorption does generally decrease as temperature increases and not run into too much trouble.
For my work, I used uncontaminated soils and solutions that were undersaturated with RDX and HMX (non-polar high explosives) and TNT (a polar high explosive). After a time which the mixtures were held at various temperatures, the supernatant and solid were both extracted and the concentrations of high explosives determined (via HPLC) - this is the adsorption part. For desorption, I used contaminated soils and DI or organic carbon-rich water (humic and fulvic acids), and repeated the experimental process. Coupled with v'ant Hoff plots, which yield enthalpies of solution (among other quantities), you can then make quantitative and qualitative statements about the nature of the interaction.
My primary reference was Voice, T. C. and W. J. Weber (1983). Sorption of hydrophobic compounds by sediments, soils and suspended solids I. Theory and background. Water Resources 17 (10): 1433-1441. I quote from my thesis below.
Physical sorption encompasses weak interactions of sorbent and sorbate, typically exhibiting heats of interaction in the 1 to 2 kcal/mol range. Bonds of this strength fall into the category of van der Waals forces, which is in turn composed of London dispersion forces and electrostatic forces.
Chemical sorption involves the formation of a much stronger bond between sorbent and sorbate, typically on the order of 15 to 50 kcal/mol. While there may be both physical and chemical sorption processes occurring simultaneously, one will commonly dominate. In fact, chemical sorption becomes more apparent at higher temperatures, when heat input into the system plays a more dominant role in the adsorption/desorption process than other factors, such as the thermodynamic gradients of hydrophobic reactions that characterize physisorption.
The electrostatic interaction of sorbent and sorbate is actually a component of physisorption. These forces are only readily apparent when the solute is polar enough to discount hydrophobic forces. A polar solute can interatct with other polar solutes, ionic species, and heterogeneous surfaces through dipole and quadrupole coupling.
The most commonly used tool in analyzing sorption equilibria is the isotherm. For the compound of interest, a plot of equilibrium solution concentration vs. solid-phase concentration (i.e., sorbed) is made at a given temperature. The resultant isotherm is best-fitted by one of a variety of sorption models. Various constants can them be evaluated from the equation that describes the fit to the data. These constants are then used to characterize the behavior of the compound of interest.