The length-scales at which thermal transport crosses from the diffusive to ballistic regime are of much interest particularly in the design and improvement of nano-structured materials. In this work, we demonstrate that the departure from diffusive transport has been observed in Si and GaAs using an optical transient thermal grating technique where an arbitrary, experimentally set length scale can be imposed on a material. In a transient thermal grating experiment, crossed laser pulses interfere creating a well-defined periodic absorption and temperature profile. A probe beam is diffracted from this transient grating and length-scale dependent thermal transport properties can be determined from the signal decay. As the length scale is decreased to lengths shorter than the mean free paths of heat carrying phonons, quasi-ballistic heat transport effects become apparent allowing us to map out length scales and mean free paths relevant to non-diffusive thermal transport in Si and GaAs.