In polymer–colloid mixtures, non-adsorbing polymers dispersed with much larger colloids provide a universal yet specific entropic attraction between the colloids. Such so-called depletion interaction arises from an osmotic-pressure imbalance caused by the polymers and is considered to be independent of temperature. Here we show that, for the most commonly used polymer–colloid depletion systems, the polymer undergoes a crossover from non-adsorbing to adsorbing and that, consequently, the effective colloidal interactions depend on temperature. We also find that a combination of the enthalpic (polymer bridging and entropic (polymer exclusion) interactions, both attractive, leads to a re-entrant regime where the colloids are dispersed and form solids both on heating and on cooling. We provide a simple model to explain the observed transitions and to fill the theoretical gap at the polymer-adsorption crossover. Our findings open possibilities for colloidal self-assembly, the formation of colloidal crystals, and the behaviour of temperature-controlled viscoelastic materials.