Basic idea
You can linear interpolate from a state $x_1$ to a state $x_2$ via
$$
x_\lambda = (1 -\lambda) x_1 + \lambda x_2 \quad (*)
$$
and $\lambda \in [0, 1]$. If you set $\lambda = 1/2$, you get the state in the middle of the $\lambda$ parameter intervall.
You could try this on the interesting parameters (translation vector, rotation angles) of your transformation matrices.
Examples
$$
T_\lambda =
\left(
\begin{matrix}
1 & 0 & 0 & (1-\lambda)x_1 + \lambda x_2 \\
0 & 1 & 0 & (1-\lambda)y_1 + \lambda y_2 \\
0 & 0 & 1 & (1-\lambda)z_1 + \lambda z_2 \\
0 & 0 & 0 & 1 \\
\end{matrix}
\right)
$$
Here you get translations by $(x_1,y_1,z_1)^T$ to $(x_2,y_2,z_2)^T$.
$$
R_\lambda =
\left(
\begin{matrix}
\cos((1-\lambda) \phi_1 + \lambda \phi_2) & \sin((1-\lambda) \phi_1 + \lambda \phi_2) & 0 & 0 \\
-\sin((1-\lambda) \phi_1 + \lambda \phi_2) & \cos((1-\lambda) \phi_1 + \lambda \phi_2) & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 \\
\end{matrix}
\right)
$$
This will rotate from $\phi_1$ to $\phi_2$ in the $x-y$-plane.
$$
S_\lambda =
\left(
\begin{matrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & (1-\lambda) s_1 + \lambda s_2 & 0 \\
0 & 0 & 0 & 1 \\
\end{matrix}
\right)
$$
This will scale the $z$-axis from $s_1$ to $s_2$.
As usual a combined transformation matrix can be calculated by matrix multiplication of the individual transformation matrices.
Other transition functions
Of course you can use other transition functions than equation $(*)$.
For visual effects on web pages so called tweening libraries became popular in the last years. That term seems to come from "in-between-ing".
Another term used for this is easing.
You might find some interesting visual effects for 2D there, which should not be hard to port to a 3D setting. See here for such a demo.
