“We have a cooling tower fan gearbox that runs very hot (more than 180 degrees F) due to the operating environment. We recently inspected the gearbox and found a lot of sludge and deposits and a strong sulfur smell. Someone suggested we use synthetic oil instead of the mineral oil currently used to prevent this from reoccurring. Would this help?”
While it is true to say that synthetic oils can be used at higher temperatures, because they do not thin out as quickly as the corresponding grade of mineral oil and provide better oxidation resistance, this may not be the best solution in this instance. This is particularly true because the sulfur smell you refer to is likely the thermal breakdown of the EP additive in the oil. Switching to a synthetic oil will do nothing to prevent thermal additive decomposition, if this is the problem.
A better solution may be to install an offline cooling system by piping out a line from the gearbox with a small gear pump to circulate the oil through an external cooling system, returning the cooled oil to the gearbox sump. Not only will this help to cool the oil and prevent thermal and oxidative breakdown, it will also have the effect of increasing the gearbox sump size, allowing the oil more opportunity to cool the gearbox.
A nice side benefit of this arrangement is that the offline system can also be equipped with a filter to help keep the oil clean and an oil sampling valve to take oil samples on a component that is often difficult to sample on the run.