Can bettas control their pigments?

[SQUIDDY12]

My Betta Benji has been wavering between little to no pigment in his fins and the bright red that he usually has. I'm not sure if this is a normal thing for bettas to do, or if it is a sign of him having some form of illness. can anyone help?

Housing
What size is your tank? i currently have a one gal bowl
What temperature is your tank? NA (not warm enough), but i will soon be going out to a heater.
Does your tank have a filter? no
Does your tank have an air stone or other type of aeration? no
Is your tank heated? no, but it will soon.
What tank mates does your betta fish live with? none

Food
What type of food do you feed your betta fish? i have betta pellets and flakes. planning on getting some brine shrimp as well
How often do you feed your betta fish? once or twice a day

Maintenance
How often do you perform a water change? once or twice a week partial, and around once a month i have done 100% water change
What percentage of the water do you change when you perform a water change? around 25%
What type of additives do you add to the water when you perform a water change? i use tap water with "splendid betta complete water conditioner"

Water Parameters:
Have you tested your water? If so, what are the following parameters? NA

Ammonia:NA
Nitrite:NA
Nitrate:NA
pH:NA
Hardness:NA
Alkalinity: NA

Symptoms and Treatment
How has your betta fish's appearance changed? The color of his tail and fins has been fading from little to no pigment and back to full color.when the color fades, his fins, tail and occasionally lower half of his body appear transparent. He also has developed black spots on his dorsal fin.
How has your betta fish's behavior changed? he's lethargic, but that is more than likely due to the water not warm enough. He also has been biting his tail and jumping out of the water.
When did you start noticing the symptoms? last night
Have you started treating your fish? If so, how? no
Does your fish have any history of being ill? no
How old is your fish (approximately)? i have had him for about 2-3 months.

I'm not sure how much this will help, but i figured i might as well add it in.
Finals finished up yesterday, so i headed home with Benji in 1.5 gal container. Needles to say that was very stressful on his behalf, being in a moving car for close to two hours. When i got home he was completely pail and not looking so well. I figured he was just shaken up from the trip, but when he wasn't back to normal a few hours later i got a little worried. It started to worry me more when he still wasn't back to normal this morning and wasn't eating. Around midday i changed out the water in his take home container with fresh water that was more warm. About ten minutes later, he was back to his full color and swimming around the surface again. I went back to check on him and hour or two later and he was practically clear again. with in a few minutes of be being there he was starting to gain his color back again. This has been happening since.
Does anyone have any information that could help me understand what is happening with my betta? thanks

[shellieca]

He definitely needs a heater. Remember his container will be cooler than your room temp so that is probably part of the problem. Also with a 1g or 1.5g volume of water more frequent water changes are needed, at least one 50% & a 100% per week, IMO. If at all possible I'd look into getting him a bigger tank preferably a 5g but a 2g would be the min suggestion. Bettas can & do change colors but don't typically go back & forth, IME, unless something is not right in their environment, mainly water conditions such as temp or bad water. More than likely he is stressed from the move & it could take him a few days to get back to his normal. Keep a close eye on him, the too cold water & the stress could make him susceptible to getting ill.