We present high angular resolution(13-26 '') large scale mapping (4' x 7') of the J=5-4, J=8-7, and J=12-11 Lines of CH3CN and (CH3CN)-C-13 and of the J=11-10 line of HC3N towards the Sgr B2 molecular cloud. All the K components of all CH3CN lines are observed in emission except towards Sgr B2M where we have detected the J=5-4, K=4 and 5=6-5, K=5 lines in absorption. CH3CN and HC3N show a ridge of strong emission along a north-south direction which contains the star forming regions Sgr B2M, Sgr B2N and Sgr B2S. The kinematics of the molecular gas shows four major molecular clouds with radial velocities of 44-54, 55-66, 67-78 and 90-120 km s(-1) and sizes of a few parsecs. The main molecular cloud with a radial velocity of 55-66 km s(-1) is observed over the whole region. Maps of the kinetic temperature and density derived from an LVG analysis of the CH3CN data are presented for the molecular clouds at 44-54, 55-66 and 67-78 km s(-1). The kinetic temperature for the three clouds ranges between 40-400 K, while the density is similar to 10(5) cm(-3) for all clouds. The total mass in these clouds is 3.10(6) M., with 70% of the mass in the 55-66 km s(-1) molecular cloud. This cloud reveals the presence of four different components: the hot cores, the warm envelope, the very hot component and the hot ring. The largest kinetic temperatures (200-400 K) are found towards the hot cores associated to the star forming regions Sgr B2M and Sgr B2N, with sizes of 0.5 and 0.7 pc respectively. Two new cores close to Sgr B2N with sizes of 0.3 pc have been found. H-2 densities for the hot cores are 10(6)-10(7) cm(-3). The mass in the cores is typically 10(3)-10(4) M.. The warm envelope extends over the whole region; this has a uniform kinetic temperature, between 40-80 K. The kinetic temperatures are higher than the dust temperatures at distances larger than 1 pc. The density in the warm envelope decreases with distance as n(H-2)=2.96.10(5) cm(-3) (r/pc)(-0.87). The analysis of the absorption lines in the J=K components of the J=5-4 and J=6-5 lines shows the presence of a hotter and more diffuse envelope probably surrounding the warm envelope. An analysis of our data gives a kinetic temperature of 300 K and a density of similar to 10(3) cm(-3). The kinetic temperature maps reveal, for the first time, the presence of a ring of hot gas (100-120 K) surrounding Sgr B2M and Sgr B2N with a radius of 2 pc and a thickness of 1.4 pc. Our data suggest that the density in the hot ring is similar to that in the warm envelope. The high temperature of the hot cores and the kinetic temperature distribution for distances smaller than I pc can be accounted for by gas-dust collisional heating. This temperature is consistent with the total luminosity of the central sources Sgr B2M and Sgr B2N. In contrast, the dust temperatures in the warm envelope are too low (10-20 K) to heat the warm envelope molecular gas by this mechanism. Heating by dissipation of turbulent motions in the envelope of Sgr B2 can explain the high gas kinetic temperatures. The presence of the hot ring suggests the existence of another heating mechanism. The morphology of the hot ring which surrounds the 50 mu m and the radio continuum emission of Sgr B2M and Sgr B2N suggests that this feature might be associated to the interface between the warm envelope and the ionized bubble created by the OB stars recently formed in the Sgr B2 core. In this interface, heating by UV photons and or shock fronts produced by the expansion of the ionized gas could explain the hot ring.
