A control system for a vehicle includes a target boost module and a turbocharger control module. The target boost module determines a target boost for first and second turbochargers based on an engine torque request. Based on a temperature of a compressor of the second turbocharger, the turbocharger control module: selectively opens a first bypass valve that regulates exhaust bypassing a first turbine of the first turbocharger; and selectively closes a cutoff valve that regulates exhaust flow through both a second turbine of the second turbocharger and a second bypass valve. The second bypass valve regulates exhaust bypassing the second turbine of the second turbocharger.