We investigate the spatial and spectral distribution of the local standard of rest (LSR) velocity resolved submillimetre emission from the warm (25-90K) gas in the Sgr A Complex, located in the Galactic centre. We present large-scale submillimetre heterodyne observations towards the Sgr A Complex covering ~300-arcmin2. These data were obtained in the frame of the Herschel EXtraGALactic guaranteed time key program (HEXGAL) with the Herschel-HIFI satellite and are complemented with submillimetre observations obtained with the NANTEN2/SMART telescope as part of the NANTEN2/SMART Central Nuclear Zone Survey. The observed species are CO(J=4-3) at 461.0GHz observed with the NANTEN2/SMART telescope, and [CI] 3P1-3P0 at 492.2GHz, [CI] 3P2-3P1 at 809.3GHz, [NII] 3P1-3P0 at 1461.1GHz, and [CII] 2P3/2-2P1/2 at 1900.5GHz observed with the Herschel-HIFI satellite. The observations are presented in a 1km/s spectral resolution and a spatial resolution ranging from 46-arcsec to 28-arcsec. The spectral coverage of the three lower frequency lines is +/-200km/s, while in the two high frequency lines, the upper LSR velocity limit is +94km/s and +145km/s for the [NII] and [CII] lines, respectively. The spatial distribution of the emission in all lines is very widespread. The bulk of the carbon monoxide emission is found towards Galactic latitudes below the Galactic plane, and all the known molecular clouds are identified. Both neutral atomic carbon lines have their brightest emission associated with the +50km/s cloud. Their spatial distribution at this LSR velocity describes a crescent-shape structure, which is probably the result of interaction with the energetic event (one or several supernovae explosions) that gave origin to the non-thermal Sgr A-East source. The [CII] and [NII] emissions have most of their flux associated with the thermal arched-filaments and the H region and bright spots in [CII] emission towards the central nuclear disk (CND) are detected. Warm Gas at very high (|Vlsr|>100km/s) LSR velocities is also detected towards the line of sight to the Sgr A Complex, and it is most probably located outside the region, in the X1 orbits.