A smart thermostat is an IoT (Internet of Things) device designed for home automation that allows remote control and monitoring, making it ideal for the library's goal of energy optimization. Smart thermostats connect to the internet, often through Wi-Fi, enabling library staff to adjust heating and cooling settings from a computer or mobile device, even when they're not on site. The ability to program and monitor the thermostat remotely can lead to improved energy efficiency and reduced costs.

Other options like 'Programmable thermostats' do not necessarily include internet connectivity, which is key for remote access. 'Basic digital thermostats' provide a digital interface but lack smart features and connectivity. 'Mechanical thermostats' are the simplest form and do not offer remote control or programming capabilities.