  Sterile neutrinos with the mass in the keV range are interesting warm dark
matter (WDM) candidates. The restrictions on their parameters (mass and mixing
angle) obtained by current X-ray missions (XMM-Newton or Chandra) can only be
improved by less than an order of magnitude in the near future. Therefore the
new strategy of search is needed. We compare the sensitivities of existing and
planned X-ray missions for the detection of WDM particles with the mass ~1-20
keV. We show that existing technology allows an improvement in sensitivity by a
factor of 100. Namely, two different designs can achieve such an improvement:
[A] a spectrometer with the high spectral resolving power of 0.1%, wide
(steradian) field of view, with small effective area of about cm^2 (which can
be achieved without focusing optics) or [B] the same type of spectrometer with
a smaller (degree) field of view but with a much larger effective area of 10^3
cm^2 (achieved with the help of focusing optics). To illustrate the use of the
"type A" design we present the bounds on parameters of the sterile neutrino
obtained from analysis of the data taken by an X-ray microcalorimeter. In spite
of the very short exposure time (100 sec) the derived bound is comparable to
the one found from long XMM-Newton observation.
