In the paper, experimental analyses of the free convection heating transfer in a flat wavy-fin heat exchanger with the dimensions of 500 × 500 mm were investigated. The experimental reserch mainly included determining the average heat flux and heat-transfer coefficient for two selected types of finned heat exchangers. First, tests were conducted for exchangers without considering the so-called ’chimney’ effect; these tests will be treated as reference studies. Then, experiments for specially designed ’chimneys’ over the exchanger with heights of 350, 850, and 1350 mm, respectively, were carried out again. The analyses were performed for an average temperature difference between the heat-exchange surface and the environment in the range of 18 to 55 K. The experimental results demonstrated that, compared to the exchanger without a chimney, the addition of a chimney significantly affects the improvement in the thermal performance of the heat exchanger under natural convection conditions. Regarding the variant without a chimney, when a chimney is used with the highest height of 1350 mm and a maximum temperature difference of 55 K, the average heat flux increases by approximately 450% and the average heat-transfer coefficient is approximately 10 times higher. The heat exchanger characterised by lower airflow resistance showed higher values of average heat flux of 5 to 45% in the Rayleigh number range of 25 to 180. Studies have indicated that in some cases, a simple modification of the geometry of the heat exchanger leads to significant improvements in thermal performance and, in extreme cases, to the elimination of supporting equipment such as fans.