We present an automated framework for online task scheduling on heterogeneous distributed systems, building on a modular parametric scheduler that enables dynamic scheduling decisions based on evolving execution states. Inspired by classical list-scheduling strategies such as HEFT and CPoP, our online scheduler simulates real-time task scheduling using only partial task graph knowledge. We evaluate our online scheduler variants against both their traditional offline baselines and a naive online strategy using a large-scale benchmark suite of real-world scientific workflows. Experimental results across different estimation methods and compute-to-communication ratio (CCR) settings show that our adaptive online schedulers consistently outperform the naive approach, achieving performance within approximately 3-5% of an ideal offline scheduler that has full future knowledge (compared to the approximately 10% overhead for the naive baseline).