The paper studies the process of drawing of glass microcapillaries from hollow cylindrical preforms, accounting for surface and gravity forces as well as for heat exchange with the surrounding medium. The quasi-one-dimensional model for hollow fiber drawing is generalized to include heat-transfer effects. The draw resonance (instability) phenomenon under non-isothermal conditions is studied and compared with the corresponding effect in the isothermal case. The method permits analysis of various flow regimes including stable steady-state drawing, sensitivity of fibers to external perturbations, drawing instability (self-sustained oscillations), and the effect of thermal conditions on the as-spun fibers. The frequency spectrum and correlation function of the time series corresponding to non-isothermal drawing are analyzed. The results show that under non-isothermal conditions (an additional degree of freedom) draw resonance continues to be a quasi-periodic phenomenon with no tendency to chaos.