It has been recently proposed that a sterile neutrino \nu _ { h } of mass m _ { h } = 40 – 80 MeV , mixing |U _ { \mu h } | ^ { 2 } \approx 10 ^ { -3 } – 10 ^ { -2 } , lifetime \tau _ { h } \mathrel { \vbox { \hbox { $ < $ } \nointerlineskip \hbox { $ \sim$ } } } 10 ^ { -9 } s , and a dominant decay mode \nu _ { h } \rightarrow \nu \gamma could be the origin of the experimental anomalies observed at LSND , KARMEN and MiniBooNE . Such a particle would be abundant inside air showers , as it can be produced in kaon decays ( K \rightarrow \nu _ { h } \mu , K _ { L } \rightarrow \nu _ { h } \pi \mu ) . We use the Z -moment method to evaluate its atmospheric flux and the frequency of its decays inside neutrino telescopes . We show that \nu _ { h } would imply around 10 ^ { 4 } contained showers per year inside a 0.03 km ^ { 3 } telescope like ANTARES or the DeepCore in IceCube . These events would have a characteristic energy and zenith-angle distribution ( E _ { \nu } \approx 0.1 – 10 TeV and \theta < 90 ^ { o } ) , which results from a balance between the reach of the heavy neutrino ( that disfavors low energies ) and a sizeable production rate and decay probability . The standard background from contained neutrino events ( \nu _ { e } N \rightarrow eX and neutral-current interactions of high inelasticity ) is 100 times smaller . Therefore , although it may be challenging from an experimental point of view , a search at ANTARES and IceCube could confirm this heavy-neutrino possibility .