Using Herschel data from the deepest SPIRE and PACS surveys (HerMES and PEP) in COSMOS, GOODS-S and GOODS-N, we examine the dust properties of infrared (IR)-luminous (LIR > 1010 L&sun;) galaxies at 0.1 < z < 2 and determine how these evolve with cosmic time. The unique angle of this work is the rigorous analysis of survey selection effects, making this the first study of the star-formation-dominated, IR-luminous population within a framework almost entirely free of selection biases. We find that IR-luminous galaxies have spectral energy distributions (SEDs) with broad far-IR peaks characterized by cool/extended dust emission and average dust temperatures in the 25-45 K range. Hot (T > 45 K) SEDs and cold (T < 25 K), cirrus-dominated SEDs are rare, with most sources being within the range occupied by warm starbursts such as M82 and cool spirals such as M51. We observe a luminosity-temperature (L-T) relation, where the average dust temperature of log [LIR/L&sun;] ˜ 12.5 galaxies is about 10 K higher than that of their log [LIR/L&sun;] ˜ 10.5 counterparts. However, although the increased dust heating in more luminous systems is the driving factor behind the L-T relation, the increase in dust mass and/or starburst size with luminosity plays a dominant role in shaping it. Our results show that the dust conditions in IR-luminous sources evolve with cosmic time: at high redshift, dust temperatures are on average up to 10 K lower than what is measured locally (z ≲ 0.1). This is manifested as a flattening of the L-T relation, suggesting that (ultra)luminous infrared galaxies [(U)LIRGs] in the early Universe are typically characterized by a more extended dust distribution and/or higher dust masses than local equivalent sources. Interestingly, the evolution in dust temperature is luminosity dependent, with the fraction of LIRGs with T < 35 K showing a two-fold increase from z ˜ 0 to z ˜ 2, whereas that of ULIRGs with T < 35 K shows a six-fold increase. Our results suggest a greater diversity in the IR-luminous population at high redshift, particularly for ULIRGs.