  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 0.1<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 SEDs with broad far-IR peaks
characterised by cool/extended dust emission and average dust temperatures in
the 25-45K range. Hot (T>45K) 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.
