For heating, you are probably better off converting to electricity (burning or fuel cell) and driving a high-COP heat pump. Good heat pumps are ~250-300% "efficient" at "converting" electricity to heat.

(Efficiency isn't in the Carnot sense, and heat pumps move heat rather than generating heat... Semantics, but point stands.)

For example: I recall reading that it is more efficient (ie BTUs generated) to use natural gas peaker plants generating electricity to drive a heat pump than to run a furnace. (Except at very low temps where COP drops quickly.)