In this paper, we study properties of the heat semigroup of configuration space analysis. Using a natural “Riemannian-like” structure of the configuration space Γ_X over a complete, connected, oriented, and stochastically complete Riemannian manifold X of infinite volume, the heat semigroup (e^{-tH^Γ})_{t\in ℝ_+} was introduced and studied in [J. Funct. Anal. 154 (1998), 444-500]. Here, H^Γ is the Dirichlet operator of the Dirichlet form \mathcal E^Γ over the space L^2(Γ_X, π_m) , where π_m is the Poisson measure on Γ_X with intensity m —the volume measure on X . We construct a metric space Γ_∞ that is continuously embedded into Γ_X . Under some conditions on the manifold X , we prove that Γ_∞ is a set of full π_m measure and derive an explicit formula for the heat semigroup: (e^{-tH^Γ} F)(γ) = ∫_{Γ_∞} F(ξ) \mathbf P_{t,γ}(dξ) , where \mathbf P_{t,γ} is a probability measure on Γ_∞ for all t > 0 , γ \in Γ_∞ . The central results of the paper are two types of Feller properties for the heat semigroup. The first one is a kind of strong Feller property with respect to the metric on the space Γ_∞ . The second one, obtained in the case X=ℝ^d , is the Feller property with respect to the intrinsic metric of the Dirichlet form \mathcal E^Γ . Next, we give a direct construction of the independent infinite particle process on the manifold X , which is a realization of the Brownian motion on the configuration space. The main point here is that we prove that this process can start in every γ \in Γ_∞ , will never leave Γ_∞ , and has continuous sample path in Γ_∞ , provided \dim X ≥ 2 . In this case, we also prove that this process is a strong Markov process whose transition probabilities are given by the \mathbf P_{t,γ}(\cdot) above. Furthermore, we discuss the necessary changes to be done for constructing the process in the case \dim X=1 . Finally, as an easy consequence we get a “path-wise” construction of the independent particle process on Γ_∞ from the underlying Brownian motion.