  In space plasmas kinetic instabilities are driven by the beaming (drifting)
components and/or the temperature anisotropy of charged particles. The
heat-flux instabilities are known in the literature as electromagnetic modes
destabilized by the electron beams (or strahls) aligned to the interplanetary
magnetic field. A new kinetic approach is proposed here in order to provide a
realistic characterization of heat-flux instabilities under the influence of
electrons with temperature anisotropy. Numerical analysis is based on the
kinetic Vlasov-Maxwell theory for two electron counter-streaming (core and
beam) populations with temperature anisotropies, and stationary, isotropic
protons. The main properties of electromagnetic heat-flux instabilities are
found to be markedly changed by the temperature anisotropy of electron beam
$A_b = T_\perp / T_\parallel \ne 1$, leading to stimulation of either the
whistler branch if $A_b > 1$, or the firehose branch for $A_b<1$. For a high
temperature anisotropy whistlers switch from heat-flux to a standard regime,
when their instability is inhibited by the beam.
