Worldwide, the known recoverable heavy oil and bitumen reserves make up more than 64% of the total reserves, of which more than 60% are trapped in carbonates. Air injection has immense potential for hydrocarbon recovery from various reservoirs. While most of the successful air-based techniques are performed within carbonate reservoirs containing light oil, theoretically, in situ combustion (ISC) has also shown great potential for recovering heavy oil and bitumen. Carbonates are complex in terms of geology and are often associated with fractures and vugs that affect the fluid flow, pressure propagation and progression of the ISC reactions. This paper describes the first experiment in which the triple-porosity concept was applied to simulate heterogeneity through artificially induced vugs, core matrix and fractures. This approach was used to study the feasibility of the ISC recovery technique for heavy oil (14° API) within a dolomite reservoir using a combustion tube (CT) in an experiment performed at 1740 psig. The combustion front advanced through 78% of the core length prior to the termination of air injection, producing 80% of the initial oil. To differentiate between the various sources of the CO2 gas (a product of carbonate decomposition vs. the combustion reaction) the atomic ratios of (CO2 + CO)/CO = 6 and (CO2 + CO)/N2 = 0.21 were applied. Additionally, partial upgrading of the produced heavy oil was observed.