  The star formation rates in starburst galaxies are orders of magnitude higher
than in local star-forming regions, and the origin of this difference is not
well understood. We use sub-mm spectral line maps to characterize the physical
conditions of the molecular gas in the luminous Galactic star-forming region
W49A and compare them with the conditions in starburst galaxies. We probe the
temperature and density structure of W49A using H_2CO and HCN line ratios over
a 2'x2' (6.6x6.6 pc) field with an angular resolution of 15" (~0.8 pc) provided
by the JCMT Spectral Legacy Survey. We analyze the rotation diagrams of lines
with multiple transitions with corrections for optical depth and beam dilution,
and estimate excitation temperatures and column densities. Comparing the
observed line intensity ratios with non-LTE radiative transfer models, our
results reveal an extended region (about 1'x1', equivalent to ~3x3 pc at the
distance of W49A) of warm (> 100 K) and dense (>10^5 cm^-3) molecular gas, with
a mass of 2x10^4 - 2x10^5 M_Sun (by applying abundances derived for other
regions of massive star-formation). These temperatures and densities in W49A
are comparable to those found in clouds near the center of the Milky Way and in
starburst galaxies. The highly excited gas is likely to be heated via shocks
from the stellar winds of embedded, O-type stars or alternatively due to UV
irradiation, or possibly a combination of these two processes. Cosmic rays,
X-ray irradiation and gas-grain collisional heating are less likely to be the
source of the heating in the case of W49A.
