A radio frequency single-electron transistor (RF-SET) based on a silicon-on-insulator (SOI) substrate is demonstrated to operate successfully at temperatures above 4.2 K. The SOI SET was fabricated by inducing lateral constrictions in doped SOI nanowires. The device structure was optimized to overcome the inherent drawback of high resistance with the SOI SETs. We performed temperature variation measurements after five thermal cyclings of the same sample to 4.2 K and found that the single-dot device transport characteristics are highly stable. The charge sensitivity was measured to be 36 microe(rms) Hz(-1/2) at 4.2 K, and the RF-SET operation was demonstrated up to 12.5 K for the first time. This work is an important prerequisite to realizing operation of RF-SETs at noncryogenic temperatures.