Does a variable speed furnace need a special thermostat?
Consequently, does Nest thermostat work with variable speed furnace?
The Nest Learning Thermostat is compatible with system fans that have one, two, or three speeds. Variable speed fans, high voltage forced air systems with fans, and proprietary systems with fans, aren't compatible with either the Nest Learning Thermostat or the Nest Thermostat E.
Keeping this in view, do I need a variable speed furnace?
meaning they are not very energy efficient. Variable-speed furnace motor — A variable speed blower motor runs at different speeds to precisely control the flow of heated air throughout your home. If you don't have a 90% efficiency or higher furnace in your home, then yes it may well be worth the cost to upgrade.
Variable speed furnace is most efficient With a variable speed furnace, the 'variable speed' doesn't refer to the furnace itself but to the furnace's indoor blower motor. Variable simply means that the blower motor operates at different speeds to more accurately control the flow of heated air to your home.