A theory of finite-size premixed flamelets (“flameballs”), in which the only processes involved are heat conduction, Arrhenius kinetics and diffusion of a light scarce reactant, is extended to account for the presence of a neighbouring cold impermeable wall. Using activation energy asymptotics we show that:(i) owing to its conductive and diffusive influences, the wall leads to two branches of stationnary, approximately spherical, flame balls when it is sufficiently remote.(ii) a non-linear equation with memory effects governs the flame radial dynamics.(iii) only a Lewis-number-dependent part of the upper branch allows for steady states that are stable against radial disturbances.(iv) along the unstable part of the upper branch, the instability is of oscillatory type.(v) by contrast to what happens when near-field volumetric losses are accounted for, no three-dimensional instability shows up.