This article presents a heuristic approach to estimate Turkey's natural gas demand based on economic indicators. The proposed heuristic methods are based on simulated annealing, which is locating a good approximation to the global optimum of a given function in a large search space. An approach based on simulated annealing is first used to forecast natural gas demand. A simulated annealing natural gas demand estimation model uses economical indicators, such as gross domestic product, population, import, and export. Linear and quadratic forms of simulated annealing natural gas demand estimation are proposed and quadratic simulated annealing natural gas demand estimation provided a better fit solution. The simulating annealing natural gas demand estimation model predicts Turkey's natural gas demand until 2025.