Is there an intensity estimation algorithm working solely in time domain
Particle velocity and sound pressure are related by the field impedance. The field impedance is a function of the media and the boundary conditions of the field.

For a reasonably shaped wave in a reasonably well behaved medium, that impedance is simply $\rho \cdot c$, i.e. density of the medium times speed of sound. For air that is about 400 Pa/(m/s). There is no phase shift and not a lot of frequency dependency.

In this case the intensity signal can be calculated as

$$I(t) = \frac{p^2(t)}{\rho \cdot c}$$

This will only get you the magnitude. Keep in mind that intensity is a vector with the same direction as the particle velocity. If you want to integrate Intensity to get actual power you need to take into account the angle between the Intensity vector and the normal vector of your integration surface. 

If you only have the pressure signal, you have to make some assumptions around the direction of the vector. Pressure is a scalar and there is no spatial information contained.