Threshold switching devices are of increasing importance for a number of applications including solid-state memories and neuromorphic circuits. Their non-linear characteristics are thought to be associated with a spontaneous (occurring without an apparent external stimulus) current flow constriction but the extent and the underlying mechanism are a subject of debate. Here we use Scanning Joule Expansion Microscopy to demonstrate that, in functional layers with thermally activated electrical conductivity, the current spontaneously and gradually constricts when a device is biased into the negative differential resistance region. We also show that the S-type negative differential resistance I-V characteristics are only a subset of possible solutions and it is possible to have multiple current density distributions corresponding to the same value of the device voltage. In materials with steep dependence of current on temperature the current constriction can occur in nanoscale devices, making this effect relevant for computing applications.