Complex diseases may result from many genetic variants interacting with each other. For this reason, genome-wide interaction studies (GWIS) are currently performed to detect pairwise SNP interactions. While the computations required here can be completed within reasonable time, it has been inconvenient yet to detect third-order SNP interactions for large-scale datasets due to the cubic complexity of the problem. In this paper we introduce a feasible method for third-order GWIS analysis of genotyping data on a low-cost heterogeneous computing system that combines a Virtex-7 FPGA and a GeForce GTX 780 Ti GPU, with speedups between 70 and 90 against a CPU-only approach and a speedup of approx. 5 against a GPU-only approach. To estimate effect sizes of third-order interactions we employed information gain (IG), a measure that has been applied on a genome-wide scale only for pairwise interactions in the literature yet.