The process to convert CO2 into long-chain hydrocarbons has been in use since the 1930s. It's not inefficient because it requires high heat. On the contrary, it produces excess heat, and must be actively cooled with water flowing through an internal heat-exchanger. The inefficiency lies in the need to create-and supply hydrogen, which requires some process such as electrolysis of water. Oh, and it does require high pressure, which costs energy. Oh and it does take energy to raise the concentration of CO2 to sufficient levels from the atmosphere while filtering out the nitrogen and oxygen. So it mostly makes more sense to start with a product like wood-gas, coal-gas or natural-gas, and then turn that into diesel. Not as interesting as pulling it from the air, but it does give you a carbon-neutral source of portable fuel, when you use plant material. It also ends up being similar to that whole "anything into oil" idea that Scientific American used to be crazy about, but turned out not to be price-competetive, and the smell of rotting turkey guys upset the neighbors.