Neutron stars can appear as sources of different nature. In this paper we address the 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 ∼106 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 ∼106 K we obtain ∼500 sources above the detection limit 0.01 cts s−1 and ∼100 easier identifiable sources with >0.1 cts s−1. Temperatures ≳1.2 × 106 K start to be in contradiction with non-detection of HOFNARs by ROSAT. Only for T ≲ 5 × 105 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.