I have a Goodman 70,000 BTU, up flow gas furnace (GMV950704CXA) with a Honeywell (RTH 7500D) thermostat installed, November 2006. The unit worked fine until outside temperature went into the 20s.

Unit fires and goes through normal sequence and runs for approximately 7 minutes, then cycles down and shuts off as though the house has reached temperature when in reality it has not. The diagnostic LED flashes 3 times indicating the low fire pressure switch is stuck open. In approximately 3 minutes the unit will again repeat this cycle. Thermostat set to 70 or more doesn’t matter, the house does not warm above 67 degrees. The filter was quite dirty (house under construction) cleaned then replaced, with no improvement. Vent and Flue pipe is new 2” X 20’ with 3 elbows and they exit horizontally through the basement wall. The drain trap is clear and functioning. When the outside temperature rises into the 30s this does not occur. There does not seem to be any obstructions in the intake or flue pipe.
I intend to get a little more into this on Saturday, any thoughts would be appreciated.

After checking the unit it was found to be over heating. The unit was installed utilizing the existing return duct from around 1952, which is too small to accommodate the high efficiency unit. When there was a call for heat during the extreme cold days, the unit needed to run longer; hence the over heating due to the undersized/ restricted return. As it’s not practical to replace or upgrade the ducts until construction / renovation is complete, slowing the variable speed motor seems to have accomplished a short term fix.

Woa woa woa. How does lowering the blower speed prevent overheating? This was the diagnostic code "The diagnostic LED flashes 3 times indicating the low fire pressure switch is stuck open"? Is the fresh air for combustion ran to the outside? I have a wild hunch... the higher blower speed was pulling too much air from around the furnace, this was affecting the pressure switch, measure the true vacuum pressure on low fire with different blower speeds.