We present ^ { 12 } CO , ^ { 13 } CO and C ^ { 18 } O J=3 \to 2 maps of the W3 GMC made at the James Clerk Maxwell Telescope . We combine these observations with Five Colleges Radio Astronomy Observatory CO J=1 \to 0 data to produce the first map of molecular-gas temperatures across a GMC and the most accurate determination of the mass distribution in W3 yet obtained . We measure excitation temperatures in the part of the cloud dominated by triggered star formation ( the High Density Layer , HDL ) of 15-30 K , while in the rest of the cloud , which is relatively unaffected by triggering ( Low Density Layer , LDL ) , the excitation temperature is generally less than 12 K. We identify a temperature gradient in the HDL which we associate with an age sequence in the embedded massive star-forming regions . We measure the mass of the cloud to be 4.4 \pm 0.4 \times 10 ^ { 5 } \mbox { M$ { } _ { \odot } $ } , in agreement with previous estimates . Existing sub-mm continuum data are used to derive the fraction of gas mass in dense clumps as a function of position in the cloud . This fraction , which we interpret as a Clump Formation Efficiency ( CFE ) , is significantly enhanced across the HDL , probably due to the triggering . Finally , we measure the 3D rms Mach Number , \mathcal { M } , as a function of position and find a correlation between \mathcal { M } and the CFE within the HDL only . This correlation is interpreted as due to feedback from the newly-formed stars and a change in its slope between the three main star-forming regions is construed as another evolutionary effect . We conclude that triggering has affected the star-formation process in the W3 GMC primarily by creating additional dense structures that can collapse into stars . Any traces of changes in CFE due to additional turbulence have since been overruled by the feedback effects of the star-forming process itself .