What size furnace does a 1600 sq ft house in Hot Springs, AR need?

Notes

• Hot Springs designs to 18°F, and that single number drives everything above. Heat loss is very close to a straight line in the indoor–outdoor difference, so a 52°F design difference gives 40.6 BTU per square foot per hour. The same house needs 49 MBH on a 35°F design day and 101 MBH at −20°F — a factor of 2.09, which is why a national "40 BTU per square foot" figure is useless in both directions.
• Two BTU numbers, and the box shows the bigger one. A 80,000 BTU/hr furnace at 96% AFUE puts 76,800 BTU/hr into the house; the rest goes up the flue. condensing, the common high-efficiency tier. The mistake to avoid is keeping the old input rating when moving to a higher efficiency — swapping an 80% unit for a 96% unit at the same input adds 12,800 BTU/hr of delivered heat the house never asked for.
• Oversizing is the expensive mistake, not undersizing. An oversized furnace satisfies the thermostat in a few minutes, shuts off, and repeats — hard on the heat exchanger and the igniter, and it leaves the house with hot-then-cold swings and cold rooms at the ends of the duct runs. Undersizing costs comfort on the four coldest nights of the year; oversizing costs comfort on all of them.
• Fuel, roughly — and it does not come from the number above. 2,928 heating degree days on a 1,600 ft² house works out to about 333 therms a season, 473 dollars at the national average gas price. That figure is calibrated against what households actually burn, not scaled from the sizing rule of thumb — and the two disagree by a factor of about 2.7, because the sizing table is deliberately conservative. Going from 80% to 96% AFUE here saves roughly $95 a year against an installed price difference usually in the $1,000–2,000 range, so the payback is a real calculation and not an obvious yes.
• This is a heat loss estimate, not a Manual J. The real one counts window area and orientation, insulation R-values, measured air leakage, ceiling height, duct location and how many people live in the house. A tight new build in Hot Springs can come in a third below this figure; a 1950s house with original windows and no wall insulation can come in a third above. Ask for the Manual J before signing — it costs a few hundred dollars on a $5,000–10,000 installation, and it is the only thing that turns the number above into a specification.
• Where the design temperature comes from. It is the 1st percentile of daily low temperatures at North Little Rock, North Little Rock Airport, 82 km from downtown Hot Springs, over 2015–2024 — the same kind of airport station ASHRAE measures at. The percentile was calibrated against eight airports with published ASHRAE values and reproduces them to within 2.2°F on average. Expect a degree or two of difference from a printed table; that is far smaller than the uncertainty in the house itself.