That sounds rough. Consider putting in air to air mini-splits instead, and leaving window cracked open, etc. As a bonus, each room will get its own thermostat, and cooling / heating.

The mini-split will only require coolant lines, and will have a sufficiently high coefficient of power that this + whatever ventilation exists might use less energy than heating with natural gas (or resistive electric), even with the loss of efficiency from not using heat exchangers.

(Doing both things would be much better, of course. Retrofitting is hard.)