We construct default-free interest rate models in the spirit of the
well-known Markov funcional models: our focus is analytic tractability of the
models and generality of the approach. We work in the setting of state price
densities and construct models by means of the so called propagation property.
The propagation property can be found implicitly in all of the popular state
price density approaches, in particular heat kernels share the propagation
property (wherefrom we deduced the name of the approach). As a related matter,
an interesting property of heat kernels is presented, too.