Furukawa et al. reported the existence of a large mass of molecular gas associated with the super star cluster Westerlund 2 and the surrounding H II region RCW49, based on a strong morphological correspondence between NANTEN2 ¹²CO(J = 2-1) emission and Spitzer IRAC images of the H II region. We here present temperature and density distributions in the associated molecular gas at ~3.5 pc resolution, as derived from a large velocity gradient analysis of the ¹²CO(J = 2-1), ¹²CO(J = 1-0), and ¹³CO(J = 2-1) transitions. The kinetic temperature is as high as ~60-150 K within a projected distance of ~5-10 pc from Westerlund 2 and decreases to as low as ~10 K away from the cluster. The high temperature provides robust verification that the molecular gas is indeed physically associated with the H II region, supporting Furukawa et al.'s conclusion. The derived temperature is also roughly consistent with theoretical calculations of photodissociation regions (PDRs), while the low spatial resolution of the present study does not warrant a more detailed comparison with PDR models. We suggest that the molecular clouds presented here will serve as an ideal laboratory to test theories on PDRs in future higher resolution studies. ; 8 page(s)