We report on an efficient and highly controlled cold atom hollow-core fiber interface, suitable for quantum simulation, information, and sensing. The main focus of this manuscript is a detailed study on transporting cold atoms into the fiber using an optical conveyor belt. We discuss how we can precisely control the spatial, thermal, and temporal distribution of the atoms by, e.g., varying the speed at which the atoms are transported or adjusting the depth of the transport potential according to the atomic position. We characterize the transport of atoms to the fiber tip for these different parameters. In particular, we show that by adapting the transport potential we can lower the temperature of the transported atoms by a factor of 6, while reducing the transport efficiency only by a factor 2. For atoms transported inside the fiber, we can obtain a transport efficiency into the fiber of more than 40% and we study the influence of the different transport parameters on the time-dependent optical depth signal. When comparing our measurements to the results of a classical transport simulation, we find a good qualitative agreement.