In polymer-colloid mixtures(1,2), non-adsorbing polymers dispersed with much larger colloids provide a universal yet specific entropic attraction between the colloids(3-8). Such so-called depletion interaction(2,3) 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(5,6), the polymer undergoes a crossover from non-adsorbing to adsorbing(9) and that, consequently, the effective colloidal interactions depend on temperature. We also find that a combination of the enthalpic (polymer bridging(10-12)) and entropic (polymer exclusion(2-4)) 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(2,9). Our findings open possibilities for colloidal self-assembly(5,13), the formation of colloidal crystals(14,15) and glasses(16), and the behaviour of temperature-controlled viscoelastic materials.