The drawing of viscous threads is important in a wide range of industrial applications, and is a primary manufacturing process in the optical fiber and textile industries.  Most of the materials used in these processes have viscosities that vary extremely strongly with temperature.

We investigate the role played by viscous heating in the drawing of viscous threads.  Usually, the effects of viscous heating and inertia are neglected because the parameters that characterize them are typically very small.  However, by performing a detailed theoretical analysis, we surprisingly show that even very small amounts of viscous heating can lead to a runaway phenomenon.  On the other hand, inertia prevents runaway, and the interplay between viscous heating and inertia results in very complicated dynamics for the system.

Even more surprisingly, in the absence of viscous heating, we find that a new type of instability can occur when a thread is heated by a radiative heat source.  By analyzing an asymptotic limit of the Navier-Stokes equations we provide a theory that describes the nature of this instability and explains the seemingly counterintuitive behavior.