  An important object of study in harmonic analysis is the heat equation. On a
Euclidean space, the fundamental solution of the associated semigroup is known
as the heat kernel, which is also the law of Brownian motion. Similar
statements also hold in the case of a Lie group. By using the wrapping map of
Dooley and Wildberger, we show how to wrap a Brownian motion to a compact Lie
group from its Lie algebra (viewed as a Euclidean space) and find the heat
kernel. This is achieved by considering It\^o type stochastic differential
equations and applying the Feynman-Ka\v{c} theorem.
