The key characteristics of superconducting materials (such as magnetic field and current density) are inversely proportional to the absolute temperature. This implies that the lowering of temperature will be accompanied by an increase in the superconducting properties of the superconducting material.
Therefore, for a superconducting magnet, the highest peak field can be obtained by operating the magnet at the lowest possible temperature. The most suitable and feasible option is superfluid helium, which can cool a system down to below 2.1 K. One of the major drawbacks of using superfluid helium, however, is the hefty energy requirement for the cooling of helium. Also, it is extremely difficult to contain supercritical helium. It can be noted that the magnets used in the Large Hadron Collider (LHC) at CERN.
If metallic superconducting materials (such as niobium-titanium or niobium-tin) are used, a temperature of 4.2 Kelvin would provide a good environment. This temperature is offered by liquid helium.