Purpose This paper aims to focus on flow boiling heat transfer in an asymmetrically heated minichannel. Two-dimensional inverse heat transfer problem was solved using the Trefftz and Beck methods. The primary purpose was to find an enhanced surface that could help intensify heat transfer. Design/methodology/approach The experimental set-up and methodology for FC-72 boiling heat transfer in two parallel vertical rectangular minichannels with smooth or enhanced heated surfaces was presented. The heat transfer coefficient was calculated using the Trefftz and Beck methods. Findings The results confirm that considerable heat transfer enhancement takes place when selected enhanced heated surface is used in the minichannel flow boiling and that it depends on the type of surface enhancement. The analysis of the experimental data revealed that the values and distributions of the heat transfer coefficient obtained using the Beck and Trefftz methods were similar. Practical/implications Many studies have been recently devoted to flow boiling heat transfer in minichannels because of the rapid development of high-performance integrated systems generating large amounts of heat. Highly efficient small-size cooling systems for new-generation compact devices are thus in great demand. Originality/value The present results are original and new in the study of cooling liquid boiling in minichannels with enhanced heated surfaces that contribute to heat transfer enhancement. The paper allows the verification of state-of-the-art methods of solving the inverse problem by using empirical data from the experiment. The application of the Trefftz and Beck methods for finding a solution of the inverse heat transfer problem is promising.