You are quite right about it being the heat, especially in a lap top not on a hard surface that kills the battery.... my experience with laptops, is they start having battery problems after about a year when they are used daily. I know a lot of people that use their laptops in bed. If you set a laptop on a bed they get very hot because of the lack of air circulation under it. I'm not sure but I think the heat can't be good for the batteries and probably helps wear them out faster.
I use my lap top plugged in to AC more than 95% of the time with the battery not even in it (except when thunder storm is approaching and I want to not be connected to the AC line.
It was essentially good as new after nearly five years of typical 8+ hours of daily lap top use (but without battery in the computer). Both the key board developed non-functional keys and then the hard drive died, but battery was still good.
I really wish they would standardize on one or two battery shapes for lap tops and sell new computer without battery at a discount. (I would put the five year old battery in the new computer and see if it would go another five years with it rarely even being inside the internally hot computer.