The main aim of this paper is to study the notion of the heat kernel associated with the zero order Mehler–Fock transform. The upper bound of the heat kernel is obtained. We discuss its some properties and fundamental solution of a generalized diffusion equation. Weierstrass type integral transform with the heat kernel is established. Further boundedness of the Weierstrass integral transform on Sobolev space is discussed and obtained its inversion formula also. Moreover we obtain Heisenberg type inequality associated with the Mehler–Fock transform and heat kernel.