I'm sorry to hear of this with your canary. It's important to note that once a canary acts ill it's already quite ill and in need of the attention of an avian-oriented vet (please see here: www.aav.org). This is a protective mechanism because sick birds are attacked by other birds in the wild. His symptoms of malaise and being puffed up ("fluffed") are important symptoms but they're not pathognomonic (specifically indicative) of any one particular disorder.
An avian-oriented vet might first treat symptomatically and supportively by providing supplemental fluids and electrolytes by needle and tube feeding a "recovery" food. Blood tests and cultures of your canary's choana - the slit between his oral cavity and nose - and cloaca (vent) may be taken. Whole body X-rays can be quite helpful as well.
I'm pleased to hear that you've heated up his environment. Placing him in an area heated to 85F by means of a 100W bulb shined into his partially covered cage (not at night when he needs to rest) or by taping a heating pad set on its lowest setting to the sides of his cage is smart. If he appears weakened remove his perches and put his food and water on the bottom of the cage along with him. I'm also pleased to hear that you began administering a water soluble avian vitamin supplement. Oasis brand is a good choice and should be added to his water at half of the recommended dose so as not to make his water distasteful. Add a calcium supplement such as Calcivet or Calciboost to his water as well. These supplements are available in pet/feed stores. Avoid over the counter antibiotics designed to be placed in his water. They won't be effective if only because an ill bird won't drink enough to medicate itself properly.
Nutritional imbalances are a common cause of illness in our pet birds. Molting is a particularly stressful time because of its nutritional demands. What has his diet consisted of, please? Seeds should compose less than 20% of his diet. Molting foods are mostly just a different mixture of seeds. A diet of mainly seed and nuts has excessive fat, carbohydrates, and phosphorus; marginal protein; adequate vitamin E, and are deficient in amino acids, calcium, available phosphorus, sodium, manganese, zinc, iron, vitamins A, D3 (necessary for efficient absorption of calcium), K, and B12, riboflavin, pantothenic acid, choline, and available niacin. Ideally, a balanced pelleted diet such as can be found here: www.harrisonsbirdfoods.com or here: www.lafeber.com/pet-birds should be fed as well as hard boiled egg yolk, pancakes and cornbread, the tops of fresh greens, dairy products such as yogurt and cheese, fresh fruits such as apples, pears, melon, kiwi, and berries, vegetables such as broccoli, carrots, beets, asparagus, cabbage, sweet potato, and squash, and even tiny pieces of meat.
Molting is evidenced by finding feathers in his cage and areas on him in which new feathers ("pin" feathers) have appeared. Respiratory infections are evidenced by an increased respiratory rate (greater than 60-80 breaths/minute), open-mouthed breathing, marked tail bobbing, or a marked respiratory effort, and abnormal sounds - squeaks, e.g. - while breathing.
Please respond with further questions or concerns if you wish.