A method of managing the heating of fluids flowing in an undersea pipe network (2-2; 2-3; 2-4) providing a connection between a surface installation and at least one undersea production well, the undersea pipe network comprising: two main pipes (8a, 8b) connected together at the sea bottom and each connected to a surface installation so as to form at least one fluid circulation loop; a plurality of secondary pipes connecting production wells to the two main pipes (8a, 8b); the method comprising connecting at least one fluid heater station (14a, 14b) to each main pipe downstream from the secondary pipes by means of a bypass pipe connected to the main pipe, and activating the heater stations in a stage of normal operation of the pipe network in order to maintain the fluids at all points of the network at a temperature higher than a predetermined temperature threshold; the pipe network (2-2; 2-3; 2-4) further comprising two connection pipes (22, 24) connecting together the two main pipes (8a, 8b) downstream from the heater stations (14a, 14b); the method further comprising, in a preservation stage of the undersea pipe network: closing the secondary pipes and the main pipes between the two connection pipes while opening the connection pipes, and activating the heater stations in order to maintain the fluids at all points in an upstream fluid circulation loop at a temperature higher than a predetermined temperature threshold; and injecting a processed fluid into the main pipes of a downstream fluid circulation loop in order to purge the fluids it contains. two main pipes (8a, 8b) connected together at the sea bottom and each connected to a surface installation so as to form at least one fluid circulation loop; a plurality of secondary pipes connecting production wells to the two main pipes (8a, 8b); the method comprising connecting at least one fluid heater station (14a, 14b) to each main pipe downstream from the secondary pipes by means of a bypass pipe connected to the main pipe, and activating the heater stations in a stage of normal operation of the pipe network in order to maintain the fluids at all points of the network at a temperature higher than a predetermined temperature threshold; the pipe network (2-2; 2-3; 2-4) further comprising two connection pipes (22, 24) connecting together the two main pipes (8a, 8b) downstream from the heater stations (14a, 14b); the method further comprising, in a preservation stage of the undersea pipe network: closing the secondary pipes and the main pipes between the two connection pipes while opening the connection pipes, and activating the heater stations in order to maintain the fluids at all points in an upstream fluid circulation loop at a temperature higher than a predetermined temperature threshold; and injecting a processed fluid into the main pipes of a downstream fluid circulation loop in order to purge the fluids it contains. closing the secondary pipes and the main pipes between the two connection pipes while opening the connection pipes, and activating the heater stations in order to maintain the fluids at all points in an upstream fluid circulation loop at a temperature higher than a predetermined temperature threshold; and injecting a processed fluid into the main pipes of a downstream fluid circulation loop in order to purge the fluids it contains.