One of my Betta's is (and has been since I bought him) in an 8g tank on his own...he loves it...
I tried a few weeks after I got him (He was my first betta) to move him from the 8g into the 3g....He lay on the bottom of the 3g on his side for about 48hrs and after this time I worried so much that I moved him back into the 8g...he was immediately cured of his "illness" and went back to swimming round happily.
Sooo, i figure from this that he noticed the size difference and was just "trying it on" to see if he could get back into his bigger tank again.
I have since added a betta to his original 3g tank...once again, going from a large lfs tank to a small 3g tank made him lie on the bottom for a few days, but as soon as he realised that he wasn't getting outa there, he soon perked up and my second betta now lives happily in this 3g tank.!
It is my advice therefore, if you move him, to do it gently, use some water (and gravel if you can) from the tank that he is in at the moment, as this will ease the transition.
Keep an eye on him, but don't worry if he doesnt behave live his normal self for a few days, persevere and show him that you're not going to be won over by any cheap tricks!
With regards to getting a heater, if you live somewhere that the temperature fluctuates a lot a night, or is fairly cold for parts of the year i would deffinately suggest getting a heater (a 25w one would be more than enough) to keep him happy at warmer temperatures!