Heatpump-based floor-heating systems for domestic heating offer flexibility in energy consumption patterns, which can be utilized for reducing heating costs—in particular when considering hour-based electricity prices. Such flexibility is hard to exploit via classical Model Predictive Control (MPC), and in addition, MPC requires a priori calibration (i.e., model identification) which is often costly and becomes outdated as the dynamics and use of a building change. We solve these shortcomings by combining recent advancements in stochastic model identification and automatic (near-)optimal controller synthesis. Our method suggests an adaptive model-identification using the tool CTSM-R, and an efficient control synthesis based on Q-learning for Euclidean Markov Decision Processes via Uppaal Stratego. This paper investigates three potential control strategy perspectives (i.e., fixed-target, target-band, and setbacks) to achieve energy efficiency in the heating system. To examine the performance of the suggested approaches, we demonstrate our method on an experimental Danish family-house from the OpSys project. The results show that a fixed-target strategy offers up to a 39 % reduction in heating cost while retaining comparable comfort to a standard bang-bang controller. Even better, target-band and setbacks strategies gain up to 46-49 % energy cost savings. Furthermore, we show the flexibility of our method by computing the Pareto-frontier that visualizes the cost/comfort tradeoff. Additionally, we discuss the applicability of Stratego for an old-fashioned binary-mode heat-pump system and report significant cost savings (33 %) as compared to the bang-bang controller. Moreover, we also present the performance analysis of Stratego against an industry-standard control strategy.