We present measurements of electrons and positrons from the semileptonic decays of heavy-flavor hadrons at midrapidity ($|y|<$ 0.35) in Au$+$Au collisions at $sqrt{s_{_{NN}}}=62.4$ GeV. The data were collected in 2010 by the PHENIX experiment that included the new hadron-blind detector. The invariant yield of electrons from heavy-flavor decays is measured as a function of transverse momentum in the range $1<p_T^e<5$ GeV/$c$. The invariant yield per binary collision is slightly enhanced above the $p$$+$$p$ reference in Au$+$Au 0%--20%, 20%--40% and 40%--60% centralities at a comparable level. This may be a result of the interplay between initial-state Cronin effects, final-state flow, and energy loss for heavy-quark production at this low beam energy. The $v_2$ of electrons from heavy-flavor decays is nonzero when averaged between $1.3<p_T^e<2.5$ GeV/$c$ from $0<{rm centrality}<40$% collisions at $sqrt{s_{_{NN}}}=62.4$ GeV. For 20%--40% centrality collisions, the $v_2$ at $sqrt{s_{_{NN}}}=62.4$ GeV is smaller than that for heavy flavor decays at $sqrt{s_{_{NN}}}=200$ GeV. The $v_2$ of the electrons from heavy-flavor decay at the lower beam energy is also smaller than $v_2$ for pions. Both results indicate that the heavy-quarks interact with the medium formed in these collisions, but they may not be at the same level of thermalization with the medium as observed at $sqrt{s_{_{NN}}}=200$ GeV.
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