We study a sample of 61 submillimetre galaxies ( SMGs ) selected from ground-based surveys , with known spectroscopic redshifts and observed with the Herschel Space Observatory as part of the PACS Evolutionary Probe ( PEP ) and the Herschel Multi-tiered Extragalactic Survey ( HerMES ) guaranteed time key programmes . Our study makes use of the broad far-infrared and submillimetre wavelength coverage ( 100 - 600 \mu m ) only made possible by the combination of observations from the PACS and SPIRE instruments aboard the Herschel Space Observatory . Using a power-law temperature distribution model to derive infrared luminosities and dust temperatures , we measure a dust emissivity spectral index for SMGs of \beta = 2.0 \pm 0.2 . Our results unambiguously unveil the diversity of the SMG population . Some SMGs exhibit extreme infrared luminosities of \thicksim 10 ^ { 13 } { L _ { \odot } } and relatively warm dust components , while others are fainter ( a few times 10 ^ { 12 } { L _ { \odot } } ) and are biased towards cold dust temperatures . Although at z \thicksim 2 classical SMGs ( > 5 mJy at 850 \mu m ) have large infrared luminosities ( \thicksim 10 ^ { 13 } { L _ { \odot } } ) , objects only selected on their submm flux densities ( without any redshift informations ) probe a large range in dust temperatures and infrared luminosities . The extreme infrared luminosities of some SMGs ( L _ { { IR } } \gtrsim 10 ^ { 12.7 } { L _ { \odot } } , 26 / 61 systems ) imply star formation rates ( SFRs ) of > 500 M _ { \odot } yr ^ { -1 } ( assuming a Chabrier IMF and no dominant AGN contribution to the FIR luminosity ) . Such high SFRs are difficult to reconcile with a secular mode of star formation , and may instead correspond to a merger-driven stage in the evolution of these galaxies . Another observational argument in favour of this scenario is the presence of dust temperatures warmer than that of SMGs of lower luminosities ( \thicksim 40 K as opposed to \thicksim 25 K ) , consistent with observations of local ultra-luminous infrared galaxies triggered by major mergers and with results from hydrodynamic simulations of major mergers combined with radiative transfer calculations . Moreover , we find that luminous SMGs are systematically offset from normal star-forming galaxies in the stellar mass-SFR plane , suggesting that they are undergoing starburst events with short duty cycles , compatible with the major merger scenario . On the other hand , a significant fraction of the low infrared luminosity SMGs have cold dust temperatures , are located close to the main sequence of star formation , and therefore might be evolving through a secular mode of star formation . However , the properties of this latter population , especially their dust temperature , should be treated with caution because at these luminosities SMGs are not a representative sample of the entire star-forming galaxy population .