Aww, super cute.
You can leave the vest in there and if he wants to use it he can. If he gets too hot he'll move to the cool side of the enclosure.
I like to keep my cool side between 18-20 at night but mine is an adult as a baby it needs a little more heat. But I also have a CHE in case she needs it by her hammock. If you can get a dimmer option for your light you can adjust the temps without having to replace bulbs. I find it quite useful between summer and winter as I can adjust to the weather if I need to.
Proper Temperatures for a Baby Bearded Dragon
Temperature Areas Ideal Temperature Range
Basking Area 95°F - 110°F (35-40 celsius)
Cool-down Area 80°F - 90°F (26-32 celsius)
Night - 70 F° to 75 F°(21-23 celsius)
Would a fan work to cool the little guy? or an ice pack in a tupperware container?
With that heat you also need to make sure it's getting proper moisture. Offer water everyday and the ever popular baths.