  In this paper we introduce a generalization of theta series in the context of
the slice monogenic function theory in $\mathbb{R}^{n+1}$ where me make use of
the so-called $*$-exponential function in a hypercomplex variable. Together
with the Eisenstein and Poincar\'e series that we introduced in a previous
paper, the theta series construction in this paper completes the fundament of
the basic theory of modular forms in the slice monogenic setting. We introduce
a suitable generalized Poisson summation formula in this framework and we apply
a properly adapted Fourier transform. As a direct application we prove a
transformation formula for slice monogenic theta series. Then we introduce a
family of conjugated theta functions. These are used to construct a slice
monogenic generalization of the third power of the Dedekind eta function and of
the modular discriminant. We also investigate their transformation behavior.
Finally, we show that these theta series are special solutions to a
generalization of the heat equation associated with the slice derivative. We
round off by discussing the monogenic case.
