A magnetic resonance apparatus having a single-circuit cooling circulation system operated with a coolant for cooling a gradient coil system so that a temperature of at least one surface of the gradient coil system remains within a prescribable temperature range. The cooling circulation system has a performance that corresponds to the average ohmic dissipated power of the gradient coil system, contains a heat exchanger that can be at least switched on and off and exhibits a high-frequency on/off switching clock. The gradient system exhibits a high average specific heat capacity and the cooling fluid exhibits an operating temperature range that proceeds beyond the prescribable temperature range.