Neutron stars can appear as sources of different nature. In this paper we address observability of a hypothetical class of neutron stars — HOt and Fast Non Accreting Rotators, HOFNARs. These objects are heated due to the r-mode instability. With surface temperatures $\sim$ 10$^6$K they are expected to be thermal soft X-ray emitters. We perform a population synthesis modeling of HOFNARs to predict the number of potentially detectable sources in the eROSITA all-sky survey. For surface temperatures $\sim$ 10$^6$K we obtain $\sim$ 500 sources above the detection limit 0.01 cts s$^{-1}$ and $\sim$ 100 easier identifiable sources with $>0.1$ cts s$^{-1}$. Temperatures $\gtrsim$ 1.2$\times$ 10$^6$K start to be in contradiction with non-detection of HOFNARs by ROSAT. Only for $T\lesssim 5 \times 10^{5} K$ numbers predicted for eROSITA turn out to be so low that identification does not look possible. We conclude that eROSITA has good chances to discover HOFNARs, if they exist. Non-detection will put very stringent limits on the properties of this type of neutron stars.