We envisage a star-topology quantum register, wherein a central computation qubit is symmetrically surrounded by a set of reset qubits. The sole objective of reset qubits is to cool the computation qubit by transferring its entropy to a heat bath with the help of heat-bath algorithmic cooling (HBAC). By combining standard NMR methods with powerful quantum control techniques, we demonstrate HBAC on two large star-topology systems, with 13 and 37 spins respectively. We obtained polarization enhancements by a factor of over 20, and an associated reduction in the spin temperature from 300 K down to less than 15 K. Exploiting the enhanced polarization of computation qubit, we prepared quantum coherences of order up to 15. Further, we have also carried out HBAC of a pair of computation qubits and use the cooled qubits to prepare an effective pure-state.