  We establish a central limit theorem for tensor product random variables
$c_k:=a_k \otimes a_k$, where $(a_k)_{k \in \mathbb{N}}$ is a free family of
variables. We show that if the variables $a_k$ are centered, the limiting law
is the semi-circle. Otherwise, the limiting law depends on the mean and
variance of the variables $a_k$ and corresponds to a free interpolation between
the semi-circle law and the classical convolution of two semi-circle laws.
