Enzymes, which are organic catalysts, operate at optimum conditions of temperature and ph. If a person has a fever, anything above normal body temperature causes denaturation of an enzyme. This means it loses its shape and its active site is no longer able to fit to its substrate properly. When this occurs, enzyme catalytic activity decreases. A fever left untreated could eventually lead to death. In this case, the protease enzymes in the gastric juice would not be able to digest protein which is the substrate as efficiently as it would under optimum conditions of temperature.
It is true that a fever increases the internal body temperature of a sick person, but the change in the body temperature caused by a fever (lets say 103 Degrees Farenheit) is not significant enough to cause much protein denaturation. One of the main digestive proteins located in the stomach is Pepsin, which digests food proteins into single peptides. Pepsin operates maximally at temperatures of 37 to 42 degrees Celsius. That is equal to 98.6 to 105 degrees Farenheit. Even if a fever were to spike above 105 Pepsin would still be able to function, just not as efficiently. Protein denaturation is not a all-or-nothing experience. If a protein is exposed to a slight change in pH that spikes above or below its optimal pH, it will not instantly denature. The more drastic the change the more drastic the denaturation. The same is true about tremperature. If Pepsin were exposed to heat slightly above 105 it would not be inactive it would simply degrade proteins at a slower and less efficient rate.