A combination of liquid-to-air and air-to-liquid heat exchangers is employed in an aircraft anti-icing system configured to avoid ice buildup on exterior leading edges of wings and engine inlets of aircraft during flight under known or anticipated icing conditions. The anti-icing system may be utilized in lieu of traditionally employed air-to-air heat exchangers. In one embodiment, a heated anti-icing liquid is conveyed through tubes juxtaposed against interior surfaces of the leading edges of the wings and engine inlets. The liquid is heated by engine core bleed air, and the tubes are arranged to optimize heat flux directly from the tubes into the leading edges of the wings and the engine inlets, respectively, to avoid ice accumulation. In one configuration, spring clips retain the tubes directly against the leading edge interiors of the wings and engine inlets, and thermal grease and insulation are used to enhance heat flux.