A cryostat was constructed using conventional and superconducting shielding techniques. The ambient magnetic field at the sample was reduced to less than 10 to the -5 Gauss. For the single crystal rhenium sample isothermal magnetization curves were obtained with thermodynamic critical fields Hc between 4mG and 0.3G. The slope of Hc(T) vs. T was found to be not constant near the zero field transition temperature To. For Hc(T))>100mG a slope of 192 G/K was obtained, while for Hc(T)~5mg the slope decreased to 88 G/K. Whether this change in slope is due to mechanical defects in the sample or due to effects of fluctuations near T0 is at present not fully determined.