The problem with that is, if you increase the temp the fan turns on to 55°C, the mean temperature is going to be higher all the time, which will directly result in most probably remaining in that upper zone anyhow, in which case you are still dealing with fan noise all the time. Lowering the point at which the fan comes on, at least with variable speed fan operation, is MORE likely to KEEP the thermal level below the point where full speed operation is necessary. This is exactly why automotive cooling systems with electric fans generally have one lower variable speed fan for a range that is lower than where it actually needs to be cooled in order to prevent overheating AND a high speed fan so that if temps still pass a certain threshold they can brute force cool the radiator.
In your case, obviously there are few options, but honestly I would consider either repasting yourself if you are handy enough to handle a teardown, or take it someplace where they can do it. Shouldn't cost more than 50 bucks or so. If it's that annoying, it's probably worth it.