Your setup does not provide the LiFePO4 battery with a proper charging profile. It also does not limit the charging current that can be drawn by the LiFePO4 battery when it is in a low state of charge.
May I suggest a DC-DC charger, which would provide the proper charging profile and isolation from the vehicle electrical system. Your temperature control system could control the DC-DC charger and warm the battery. However most LiFePO4 battery BMS systems provide the low temperature charging lockout and some cold weather rated batteries have a built-in heater.
Most Lifepo4 batteries dont have low temp protection and even fewer have internal heating. This works well and its simple.