We present an experimental study of thermal conduction in 1 μm thick suspended CVD diamond film by time-domain thermoreflectance (TDTR), an optical pump-probe technique. Important aspects of signal analysis and measurement sensitivity are discussed, outlining the various thermal metrology challenges posed by this system. We measure the properties of the near-interfacial coalescence region and high-quality growth region by performing experiments on the bottom and top sides of the suspended film, respectively, and find that the small average grain size of the former, and strong columnar anisotropy of the latter region are reflected in the measurements of thermal conductivity. Our TDTR methodology utilizes the information present in both the amplitude and phase response of the system at the modulation harmonic of the pump laser, in order to separate out the effects of the transducer-diamond thermal boundary conductance from the intrinsic diamond conductivity. Additionally, measurements are made across a range of modulation frequencies in order to obtain better estimates of the conductivity anisotropy. For the 1 μm thick film, we estimate an in-plane to through-plane anisotropy ratio of 0.3, and through-plane conductivities of 440 W/m-K and 140 W/m-K for the high quality and coalescence regions, respectively.