This study investigates the inviscid, linear spatio-temporal stability of heated, compressible, and incompressible coaxial jet flows. The influence of the temperature ratio and the velocity ratio between the core jet and the bypass stream on the transition from convectively to absolutely unstable flows is studied numerically. The investigation shows that for coaxial jets, absolute instability can occur for considerably lower core-stream temperatures than for single jets. The reason for this modified stability character is the appearance of an additional unstable mode as a result of the outer velocity shear layer between the bypass stream and the ambient flow. The presence of two shear layers enables the interaction between otherwise free waves to give rise to new instabilities. When the bypass-stream velocity is increased, the classical absolute mode known from single jets (inner mode) is first stabilized and then destabilized for high bypass-stream velocities, whereas the outer mode reaches maximum spatio-temporal growth rates when the core-stream velocity is approximately equal to twice the bypass-stream velocity. Additionally, it is demonstrated that the spatio-temporal character of the modes is very sensitive to the shear-layer thickness and to the distance separating the two layers. Increasing the Mach number strongly dampens the onset of an absolute instability for both modes.