Smart thermostats have been proposed as a way to reduce energy consumption in the home. While occupancy-based thermostat control and scheduling has been shown to provide energy savings, more recent work in comfort-aware thermostats promises to provide even greater savings. Comfort awareness and adaptive thermal comfort models, combined with the mixed-initiative eco-coaching approach to thermostat control, offer a promising approach to optimizing savings by offering both schedule and setpoint recommendations and actionable plans. In this paper, we investigate the design space of comfort-aware eco-coaching thermostats. Through a user enactment study wherein 11 participants encountered fifteen design probes covering various design attributes and interaction scenarios, we uncover insights on how to design such thermostats in a way that respect people's values relating to comfort, sustainability, control, convenience, and allocation of agency while also encouraging more energy efficient behaviors.