Specifically, each element has a random key associated with it in addition to its priority (which changes as a continuous function of time as in all kinetic data structures).
The kinetic heater is then simultaneously a binary search tree on the element keys, and a heap on the element priorities.
In practice however, it is less efficient since the extra random keys need to be stored, and the procedure to handle certificate failure is a (relatively complicated) rotation instead of a simple swap.
[1] If every element has a key and a priority associated with it, then there is a unique tree structure that is simultaneously a search tree on the keys and a heap on the priorities - this structure corresponds to the treap (if the priorities are randomly chosen) or the kinetic heater (if the keys are randomly chosen).
When a certificate on an edge fails, a kinetic heater will perform a rotation around the nodes that failed (instead of the swap that a kinetic heap would perform).