Thermal lensing with a CW pump in materials with large extinction coefficient is used to convert a probe beam with Gaussian transverse intensity profile into a ring-shaped beam with dark core. The radius of the dark core can be controlled by varying the pump power. A Mach-Zehnder interferometer was used to study the beam's phase profile. A theoretical analysis of the phase profile yields estimates of the threshold pump power needed to generate a dark core and the maximum change of the refractive index achieved in the experiment. As an application of the dark core beam, a numerical simulation of the effect has been combined with the experimental data to get a quick in situ estimate of thermal conductivity by a non-contact method. © 2020 Elsevier Ltd