Thermal cooling performances of extremely lightweight mechanical carbon fiber support structures with an integrated liquid cooling system for monolithic silicon pixel detectors have been investigated. The high heat removal efficiency using single-phase liquid flow is shown for a power density up to 0.5 W/cm². These solutions provide therefore possibility to build a detector with a record radiation length of 0.3% per layer, ensuring considerable extensions of the physical program of investigations of the quark-gluon plasma in ultra-relativistic heavy-ion collisions at the Large Hadron Collider.