My '08 HS Sov II holds 355 gallons and has a 6 kW heater. The calculated temperature rise is 6.9°F per hour with the cover on. Real-world observations have confirmed this. Very cold ambient temps will lower this rate by a tenth or two of a degree per hour. I've never had a reason or desire to calculate/measure rate of rise with the cover off since that would be very inefficient. As has been stated, there are many other variables that come into play when the cover is off such as...
- Shell color and heat load from the sun (the slowest rise will result with no direct sun or a light color shell, the fastest rise will result with direct sun and a dark color shell)
- Ambient temperature (this is pretty obvious - the colder it is, the longer it will take to heat the water. If the heater is too small, it won't heat at ALL with the cover off if the heat loss is equal to or greater than the heater capacity. Most 110V units have this problem because their heater wattage is limited to no more than 1.5 kW.)
- Wind speed (wind speeds up evaporation, which absorbs heat)
- Humidity (lower humidity = faster evaporation = more cooling, higher humidity = slower evaporation = less cooling)
- Jet/bubbler usage (injecting air into the water will cool it off - some brands like HS slightly preheat the air stream using waste heat from the jet pumps for slightly better efficiency)
- Occupancy (more heat-producing bodies will help raise the temperature of the water...IF it is less than 98.6°F)