  Chernoff approximations are a flexible and powerful tool of functional
analysis, which can be used, in particular, to find numerically approximate
solutions of some differential equations with variable coefficients. For many
classes of equations such approximations have already been constructed since
pioneering papers of Prof. O.G.Somlyanov in 2000, however, the speed of their
convergence to the exact solution has not been properly studied. We select the
heat equation (because its exact solutions are already known) as a simple yet
informative model example for the study of the rate of convergence of Chernoff
approximations. Examples illustrating the rate of convergence of Chernoff
approximations to the solution of the Cauchy problem for the heat equation are
constructed in the paper. Numerically we show that for initial conditions that
are smooth enough the order of approximation is equal to the order of Chernoff
tangency of the Chernoff function used. We also consider not smooth enough
initial conditions and show how H\"older class of initial condition is related
to the rate of convergence. This method of study in the future can be applied
to general second order parabolic equation with variable coefficients by a
slight modification of our Python 3 code.
  This arXiv version of the text is a supplementary material for our journal
article. Here we include all the written text from the article and additionally
all illustrations (Appendix A) and full text of the Python 3 code (Appendix B).
