  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.
