Heavy utility bikes aren't a problem unless climbing steep hills. Leaning forward and not allowing for natural body cooling are the two primary causes of sweat. Most moderately fit people can ride an upright Dutch bike for several miles at 10-13 MPH and get no more sweaty than walking from their car to the building they work in. If the temp & dew point are not enough to cause you to sweat walking then they will not cause you to sweat riding upright at a moderate pace. In many cases riding upright will keep you cooler than walking. This is all assuming normal street/work clothes btw.

Helmets, and to some extent gloves, cause very considerable sweating as they keep your body from being able to cool itself properly. Your head is likely the number one heat radiator of your body and sticking a helmet on it prevents this just the same as covering the radiator on your car.

If you are doing a 25 mile training ride then go for the road bike, helmet, and all the other kit just as with any other sport or workout and plan to shower after. If you are riding for transportation then do so in a way that is much simpler, more comfortable, and does not produce excessive sweat.