The minimum of 290 kts is "the minimum airspeed required to maintain appropriate
cabin pressure differential with the outflow valve in the full open position" according to our Flight Manual.
Now regarding the Pack output temps, the following note is in our Flight Manual:
Pack valves may have failed in full open (hot) position.
Note: Flight deck and cabin temperatures may increase rapidly
below 290 knots depending on pack valve position.
This is under both the B737-700 and the B737-800/900. Now, I ass-u-ming that they meant to say Mix Valve failing full HOT or maybe Temp Ctrl Valve (-8/900) failing open. Maybe these would cause a Pack Trip and then the 290 kts minimum is to get enough Ram Air across the Heat Exchangers to cool things down. Otehrwise, I can't quite figure out why they referenced the Pack Valves. These Flight Manuals can be so cryptic sometimes....or maybe it is very simple - but I'm just tired!