Initially branded as dedicated graphics processing accelerators, GPUs now find applications in an ever-growing range of domains, including artificial intelligence, high-performance computing, self-driving vehicles, and bioinformatics. However, this diversity comes at the cost of reduced resource efficiency and micro-architectural affinity. Evidently, the homogeneity of the GPU hardware struggles to cope with the vast heterogeneity of GPU applications. Motivated by the aforementioned observations, this article introduces the concept of Single-ISA Heterogeneous GPU architectures. In order to explore the efficiency of the new GPU architectural paradigm, we extend Accel-Sim, the state-of-the-art, cycle-accurate GPU simulator to support single-ISA heterogeneous cores within the GPU chip. The proposed implementation, called AccelHSA, supports independently tuning the micro-architectural characteristics of the cores, unlocking a wide design space. The CUDA API is extended to allow control of the kernel-to-core-type mapping along with a newly developed kernel launching model that supports concurrent execution, aimed at, albeit not limited to, the context of the simulator. We showcase the impact of single-ISA heterogeneous GPU architectures via a case study targeting the collocation of resource sensitive and insensitive HPC kernels. Finally, the heterogeneous GPU architecture is evaluated against homogeneous GPU baselines, demonstrating a 27.07% average speedup with a marginal 0.47% area overhead.