I assume you are referring to the 4ft F25T12. The reason that lamp can’t be used on commercial ballasts has nothing to do with the capacitor or the ballast itself. The “F25T12” is nothing more than a regular F40T12 with weaker electrodes that can’t handle as much power. It’s a F40 that is designed to be underpowered. This renders it incompatible with commercial ballasts which are usually “normal ballast factor” (operate lamps at their rated power). The F25T12 would operate at 40W in this configuration, causing early failure. Residential ballasts are usually “low ballast factor,” and typically operate F40T12 lamps at 25W or less, meaning the F25T12 gets its designed power and will last its rated life.
F40T12 34W lamps will cause any ballast to run warmer, residential or commercial. In fact, earlier residential ballasts were known to get unbelievably hot with energy-saving lamps. I believe this is because the 34W lamps cause actually draw more power on LPF ballasts than 40W lamps do, which causes the ballast to operate well above its rated power and temperature. Later models like the Advance HB-234-TP were designed to handle 34W lamps better, but you should never run a 34W F40 on any residential ballast that does not say it is compatible with one. Same goes for HPF commercial ballasts. Many units from before the 1980s were not designed for energy-saving lamps and would overheat with them, so just check your ballast before installing them. Newer ones are usually OK with them.