Using Herschel data from the deepest SPIRE and PACS surveys (HerMES and PEP) in COSMOS and GOODS (N+S), we examine the dust properties of IR-luminous (L_IR>10^10 L_sun) galaxies at 0.145K) SEDs and cold (T<25K), 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[L_IR/L_sun]=12.5 galaxies is about 10K higher than that of their log[L_IR/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 10K lower than what is measured locally. This is manifested as a flattening of the L-T relation, suggesting that (U)LIRGs in the early Universe are typically characterised 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<35K showing a 2-fold increase from z~0 to z~2, whereas that of ULIRGs with T<35K shows a 6-fold increase.
