Cyclic thermal stresses produced by rf pulsed heating can be the limiting factor on the attainable reliable gradients for room temperature linear accelerators. This is especially true for structures that have complicated features for wakefield damping. These limits could be pushed higher by using special types of copper, copper alloys, or other conducting metals in constructing partial or complete accelerator structures. Here we present an experimental study aimed at determining the potential of these materials for tolerating cyclic thermal fatigue due to rf magnetic fields. A special cavity that has no electric field on the surface was employed in these studies. The cavity shape concentrates the magnetic field on one flat surface where the test material is placed. The materials tested in this study have included oxygen free electronic grade copper, copper zirconium, copper chromium, hot isostatically pressed copper, single crystal copper, electroplated copper, Glidcop®, copper silver, and silver plated copper. The samples were exposed to different machining and heat treatment processes prior to rf processing. Each sample was tested to a peak pulsed heating temperature of approximately 110°C and remained at this temperature for approximately 10×10^{6} rf pulses. In general, the results showed the possibility of pushing the gradient limits due to pulsed heating fatigue by the use of copper zirconium and copper chromium alloys.