As a person of Dutch heritage, I'm pretty familiar with the negative consequences of excessive sun exposure. For me, that's about 15 minutes.
To the best of my knowledge, there's nothing about melanin production that would make you sluggish. In a sunny climate, exposure to the heat and the brightness of the sun can make you feel run down and cause headaches.
If you're sunburned, then you're not likely to feel good because your body is fighting to heal itself from the burn.
To sum up, it's not the melanin per se, but all the changes that your body needs to make in order to adjust to the sunnier climate. Drink plenty of water, rest as much as you need to, and avoid sunburn. Other than that, relax and soak up some rays!