It would be more thermally efficient, but not as economically efficient. Firstly, consider the capital costs of an engine + natural gas pipeline + heat pump (e

It would be more thermally efficient, but not as economically efficient. Firstly, consider the capital costs of an engine + natural gas pipeline + heat pump (excluding electrical motor) versus either a natural gas pipeline + burner _or_ a heat pump + electric motor. A high guess on the lifetime of a suitable natural gas engine under consumer quality maintenance (variable and generally late) would be 10,000 runtime hours. On heating duty cycle that's about 5 years. You can reduce runtime hours with more starts and stops, but that reduces the engine life -- probably more than it saves. So the extra capital costs of the engine must amortize over five years out to less than the lost efficiency. Importing electricity has economies of scale in capital costs. Direct burning of natural gas has low capital costs. Secondly, there's the efficiency question. A moderate-sized heating system has a peak power of around 100,000 BTU/hr or about 29 KW. That's about 37 horse power. Engines of that size are piston engines with around 20% efficiency. Therefore out of every 5 units of fuel-heat you get 1 unit of mechanical energy you have 4 units of waste heat. That mechanical energy put through a heat pump will net you around 3 units of heat for a total of 7 units of heat for every 5 units of fuel. That's better than just burning it, but 140% thermal efficiency is only ~45 points better than a natural gas furnace and comes with much higher maintenance costs (oil changes, filters, etc.). Importing electricity has economies of scale in production, even if generated using natural gas, because the 'engines' are of more efficient types with 40-60% thermal efficiency. Further, an electric motor is low maintenance and long lasting. So for every 5 units of fuel-heat in a power plant you can get between 6 and 9 units of heat through an electrical heat pump. Not too different overall, but with much lower per-house capital and maintenance costs. So compared to a natural gas furnace it's not a win because of the capital costs and maintenance costs versus the much cheaper equipment; a ~$3000 engine every five years is $600 per year, which buys a lot of natural gas. Compared to an electric heat pump it's not a win because the efficiency of engines that small aren't great.