Sounds like DOSBox is running full tilt, causing your CPU to get hot, which kicks the cooling fan for it into high gear. As TFH suggested, bring up your CPU usage graph (Ctrl+Alt+Delete), and under the "Performance" tab, see how much DOSBox is using in the "CPU Usage" line. If you have a single core CPU, see how close it is to 100%. If it's a hyperthreading CPU, see how close to 50% it is. If it gets close to those numbers often, then there is why your cooling fan is cranking up.
Just out of curiosity, when was the last time you gave the inside of your PC a cleaning? If it's been a while, there's probably dust collecting in there that's causing your CPU to heat up quicker than normal. Might wanna give it a cleaning if that's the case.
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