Fluid connection/heating device (1, 1') comprising: - an external connector (40, 40') inside which are formed: * a first channel (41, 41') extending along a first symmetry axis from a first orifice (O1, O1') of the connector and intended to convey a first fluid to be heated, and * a second channel (42, 42') surrounding said first channel and intended to convey a second heat transfer fluid, said second channel comprising a radial flow section (44, 44') for the second fluid, that extends along a second axis perpendicular to said first axis and an axial flow section (45, 45') for said second fluid that extends said radial section along said first axis to a second orifice (O3, O3') of the connector coaxial with said first orifice; and - a tubular connection insert (50, 50') that is mounted along said first axis inside the connector, and is adapted to connect said first orifice to a first pipe that coaxially extends said first channel out of said second orifice, by a first end (51, 51') of the insert adjacent to said first orifice and a second end (52, 52') of the insert adjacent to said second orifice, respectively, the insert defining, inside the connector: * an inner conduit of the insert that partially defines said first channel, and * said axial section, having an annular cross section that forms radially between the insert and a tubular wall (46, 46') of the connector, which extends along said first axis to said second orifice; the first fluid flowing through the insert being heated by the second fluid, the insert being configured to be mounted by sliding through said second orifice from an intermediate non-connection position of the device in which said second end of the insert is axially located inside said second orifice, to a final connection position of the device in which said second end of the insert is axially located towards the inside of said second orifice, characterised in that said first end (51, 51') of the insert (50, 50') is mounted against said tubular wall (46, 46') of the connector (40, 40') in said intermediate position, and in a sealed manner against said first orifice (O1, O1') in said final position. - an external connector (40, 40') inside which are formed: * a first channel (41, 41') extending along a first symmetry axis from a first orifice (O1, O1') of the connector and intended to convey a first fluid to be heated, and * a second channel (42, 42') surrounding said first channel and intended to convey a second heat transfer fluid, said second channel comprising a radial flow section (44, 44') for the second fluid, that extends along a second axis perpendicular to said first axis and an axial flow section (45, 45') for said second fluid that extends said radial section along said first axis to a second orifice (O3, O3') of the connector coaxial with said first orifice; and * a first channel (41, 41') extending along a first symmetry axis from a first orifice (O1, O1') of the connector and intended to convey a first fluid to be heated, and * a second channel (42, 42') surrounding said first channel and intended to convey a second heat transfer fluid, said second channel comprising a radial flow section (44, 44') for the second fluid, that extends along a second axis perpendicular to said first axis and an axial flow section (45, 45') for said second fluid that extends said radial section along said first axis to a second orifice (O3, O3') of the connector coaxial with said first orifice; and - a tubular connection insert (50, 50') that is mounted along said first axis inside the connector, and is adapted to connect said first orifice to a first pipe that coaxially extends said first channel out of said second orifice, by a first end (51, 51') of the insert adjacent to said first orifice and a second end (52, 52') of the insert adjacent to said second orifice, respectively, the insert defining, inside the connector: * an inner conduit of the insert that partially defines said first channel, and * said axial section, having an annular cross section that forms radially between the insert and a tubular wall (46, 46') of the connector, which extends along said first axis to said second orifice; * an inner conduit of the insert that partially defines said first channel, and * said axial section, having an annular cross section that forms radially between the insert and a tubular wall (46, 46') of the connector, which extends along said first axis to said second orifice;