Single-stranded (ss)RNA viruses are thought to evolve rapidly due to an inherently high mutation rate. However, it remains unclear how ssRNA viruses adapt to novel environments and/or how many and what types of substitutions are needed to facilitate this evolution. In this study, we followed the adaptation of the ssRNA bacteriophage Qβ using thermally adapted Escherichia coli as a host, which can efficiently grow at temperatures between 37.2 and 45.3 °C. This made it possible to evaluate Qβ adaptation to the highest known temperature that supports growth, 45.3 °C. We found that Qβ was capable of replication at this temperature; within 114 days (~1260 generations), we detected more than 34 novel point mutations in the genome of the thermally adapted Qβ population, representing 0.8% of the total Qβ genome. In addition, we returned the 45.3 °C-adapted Qβ populations to 37.2 °C and passaged them for 8 days (~124 generations). We found that the reverse-adapted Qβ population showed little to no decrease in fitness. These results indicate that Qβ can evolve in response to increasing temperatures in a short period of time with the accumulation of point mutations.