The invention relates to a pump housing (2) comprising a dual-wall casing (3) which enables a first fluid (4) to flow at least partially around a compression chamber (5) for compressing a second fluid (6), said compression being performed with at least two elongated rotors (7, 8). The dual-wall casing (3) comprises: (i) a first wall (10) which defines the volume of the compression chamber (5), and (ii) a second wall (11) which extends around the first wall (10) at a distance (12) from same such as to enable the first fluid (4) to flow therethrough. The pump housing (2) consists of two subassemblies (13, 14), namely a first subassembly (13) and a second subassembly (14), which are assembled along a sealing surface (15) that is essentially orthogonal to the longitudinal axes (70, 80) of the rotors (7, 8). Both the first subassembly (13) and the second subassembly (14) are characterised in that they consist of a rigid element (16) which is moulded from a first thermally-conductive material and which comprise two opposing faces, namely a first face (18) and a second face (19). According to the invention, the above-mentioned first wall (10), which is moulded with the rigid element (16), is disposed beyond the first face (18) such as to extend essentially orthogonally thereto, while the second wall (11) is also disposed beyond the first face (18) such as to extend essentially orthogonally thereto, but in parallel to a fourth face (21) of the first wall (10) without being joined to same. In addition, cut-outs (23) are recessed into the first face (18) such that each cut-out forms at least one housing for a first member (9) that is used to guide the rotation of one of the opposing ends (71, 72, 81, 82) of one of the rotors (7, 8).