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The LHC accelerator will employ 1800 superconducting magnets (for guidance and focusing of the particle beams) in a pressurized superfluid helium bath at 1.9 K. This temperature is a severely constrained control parameter in order to avoid the transition from the superconducting to the normal state. Cryogenic processes are difficult to regulate due to their highly non-linear physical parameters (heat capacity, thermal conductance, etc.) and undesirable peculiarities like non self-regulating process, inverse response and variable dead time. To reduce the requirements on either temperature sensor or cryogenic system performance, various control strategies have been investigated on a reduced-scale LHC prototype built at CERN (String Test). Model Based Predictive Control (MBPC) is a regulation algorithm based on the explicit use of a process model to forecast the plant output over a certain prediction horizon. This predicted controlled variable is used in an on-line optimization procedure that minimizes an appropriate cost function to determine the manipulated variable. One of the main characteristics of the MBPC is that it can easily incorporate process constraints; therefore the regulation band amplitude can be substantially reduced and optimally placed. An MBPC controller has completed a run where performance and robustness has been compared against a standard PI controller (Proportional and Integral).