I would say your main problem would be getting a happy medium between 'temporary' as in removing your work should you wish to sell, and investing money in insulating it for comfortable use. We converted an outhouse in a previous house to a habitable room, with consent and under Building Regs. We had to insulate all walls, ceiling and floor and used Kingspan. No problem because it keeps it warmer and was a permanent change. But it was a fair bit of expense and work and not something I'd entertain if I was viewing it as temporary.
I'd be inclined to ask advice of Building Control at your council. They are, as stated here, very helpful. Because of the comfort factor, and despite the fact it helps that your garage is integral, I think you would be wiser to convert it properly and with consent. A future buyer can decide what he wants to do regarding it's use and need only remove the door insulation and boarding to reinstate it as a garage. But you will have provided maximum comfort for your use of it as a games room. I would suggest that should it go on the market then converted properly, with or without garage door, it would add value if a buyer prefers an extra room.
If you don't do it properly you may find it uncomfy, slow and expensive to heat, and in colder months you'll prefer to be in front of the tv instead!