We present a CO(3-2) survey of selected regions in the M31 disc as part of the JCMT large programme, HARP and SCUBA-2 High-Resolution Terahertz Andromeda Galaxy Survey (HASHTAG). The 12 CO(3-2) fields in this survey cover a total area of 60 arcmin(2), spanning a deprojected radial range of 2-14 kpc across the M31 disc. Combining these observations with existing IRAM 30m CO(1-0) observations and JCMT CO(3-2) maps of the nuclear region of M31, as well as dust temperature and star formation rate surface density maps, we are able to explore the radial distribution of the CO(3-2)/CO(1-0) integrated intensity ratio (R-31) and its relationship with dust temperature and star formation. We find that the value of R-31 between 2 and 9 kpc galactocentric radius is 0.14, significantly lower than what is seen in the nuclear ring at 1 kpc (R-31 similar to 0.8), only to rise again to 0.27 for the fields centred on the 10 kpc star forming ring. We also found that R-31 is positively correlated with dust temperature, with Spearman's rank correlation coefficient rho = 0.55. The correlation between star formation rate surface density and CO(3-2) intensity is much stronger than with CO(1-0), with rho = 0.54 compared to -0.05, suggesting that the CO(3-2) line traces warmer and denser star forming gas better. We also find that R-31 correlates well with star formation rate surface density, with rho = 0.69.