We present 12CO, 13CO and C18O J= 3 → 2 maps of the W3 giant molecular cloud (GMC) made at the James Clerk Maxwell Telescope. We combine these observations with Five College Radio Astronomy Observatory CO J= 1→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), 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 ± 0.4 × 105 M⊙, in agreement with previous estimates. Existing submillimetre 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, , as a function of position and find a correlation between 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.