Heat does kill batteries, but it helps to kill them faster when they are never fully charged, but instead live their life somewhere below that ideal.
While I am urinating into the wind on this topic on this forum, Defects aside, the best constructed battery kept chronically undercharged will not last as long as the worst consructed battery kept fully charged.
And While One can deplete a 100% charged battery to 80% charged in 10 minutes of blasting ther stereo with the engine off, it takes no less than 3.5 hours, assuming ideal voltages sought and held, for that 80% charged battery to return to 100% charged.
And here's some special news for those with ultimate confidence in their alternators 130 amp rating, An 80% charged battery at 13.7v might accept 10 amps, but at 14.7v might accept 25 amps, and the only way that the 130 amp rating of the alternator will be employed is if it is cold, spinning fast, with 100 amps of DC loads other than a depleted batttery asking it to work.
Alternators are contolled by their voltage regulators. they make as much amperage (upto their limit at their rpm) as required to attain and hold the voltage the VR is seeking. The battery accepts as much amperage as it wants at the voltage reachingn the battery terminals, and the more charged the battery is, the less amperage required to bring the battery upto higher voltages.
You cannot force a battery to accept more than it wants to accept other than by raising the voltage( electrical pressure), and raising voltage much over 15 on a 12v lead acid battery is abusive.
Most vehicle VR's are timid, and will prematurely drop to mid 13's for fear ov overcharging, and fully charging a battery at 13.6v, from 80% charged, takes no less than 12 hours, and if it is an older battery 13.6 will likely NEVER maximize the specific gravity of the battery and thus never be able to fully charge it, asn as a result it degrades even faster.
Regarding short trip driving, this is only really an issue when the battery is not fully charged to begin with for the reasons stated above, as it takes a long time to fully charge a battery and this cannot be sped up. To speed up charging one would have to increase voltage beyond 15 volts and this is extremely abusive to the battery, and it would still take a long time for specific gravity to max out indicating a fully charged battery.
However the time it actually takes the alternator, at 14.7v, to recharge what was used by the starter to start a modern fuel injected engine, takes less than a minute.
I have an AGM battery, and when new when and when it was absolutely top charged it would accept 0.0x amps at 14.7v. So I can start my engine from this absolutely fully charged state, and once started my VR allows my alternator to produce enough amperage to reattain 14.7v. Once amps taper to 0.0x again at 14.7, the battery is again fully charged. I have timed this at 45 seconds multiple times. So in order to short change my battery by short trip driving, I would have to start my engine and drive for less than 45 seconds before shutting the engine off.
So short trip driving never has a chance to fully charge a battery, but a fully charged battery that is depleted only be engine starting, is not going to be affected by short trip driving unless some other loads are depleting the battery below 100%, then short trip driving will never have enough time, and likely nowhere near enough voltage, to ever fully charge the battery, and as a result, it dies very prematurely.
And Instead of the battery owner realizing the chronic undercharging of the battery, in combination with the heat the battery was forced to endure as being responsible for the premature demise of the battery, they actually think the sticker on the battery is responsible.
So instead of blaming poorly made batteries, and their labels, one should understand the lead acid battery always wants to be fully charged, and kept cool. This ideal is of course impossible, but the maintenance minded Bitogers should know that their vehicles charging system will likely never be able to actually fully charge the battery, and take steps to insure that the battery is fully charged by other means.
Now the inabiulity of so called smart chargers to complete that task is another issue, as they too will drop voltage prematurely, but they will get the battery much closer to a true 100% state of charge than the vehicles charging system, and will greatly lengthen the rental contract on the battery, if the user decides to use one.
One cannot really do much if anything abnout the heat the battery is subjected to, buut they can do a lot in termis of average state of charge of the battery, especially once they realize their vehicles charging system only cares about not overcharging the battery.
And Some newer vehicles, in an attempt to eek out slightly higher fuel economy, will actually deliberately discharge the battery, so that it can accept larger amperages when teh VR decides to ask for 14.5v.
Each 25 amps the alternator is asked to produce sucks up about 1 HP from the engine, so if they keep the batery at 75% charge, when voltage is bumped upto 14.7v the battery might be able to suck up 40+ amps.
So thay have the VR ask for 14.7 only when one lets off the gas or hits the brakes, and then keeps it at ~12.7 volts the rest of the time to keep the battery low enough that it can then accept higher amperage when the voltage is increased.
This 'regenerative' braking scheme in modern vehicles in the quest for that 0.02 MPG increase, wastes much more total energy in teh recycling and redistribution of lead acid batteries which fail very prematurely because they are deliberately kept undercharged and thus die extremely prematurely because of it.
Vehicles that employ this strategy will always have extremely short battery life, and the owner of such a vehicle might not see much benefit from hooking their battery to a charger regularly, as the next time it is driven the VR will not be seeking to hold the battery fully charged.
But the battery which is fully charged, even if only briefly before the vehicles asinine voltage regulation intentionally seeks to deplete the battery, will retain its capacity for somewhat longer.
So the end user whose vehicle does noot employ this 'regenerative braking' MPG incrememtal boost, can greatly effect their battery ongevity by ensuring the battery is fully charged by other means. But battery heat is also a killer.
Just know that the vehicle manufactuer does not care about battery life, they care about not overcharging it, as an overcharged battery produces flammable gasses. Voltage regulation is timid and will not fully ccharge a battery, and some modern vehicles in the attempt to eek out slightly more MPGs to meet CAFE, will deliverately sacrifice battery life to do so and it will not matter much if you buy the freshest East Penn battery you can find or the cheapest wally world valuepower battery as neighter is going to be made happy by the charging sources it sees
Anyway, over the last 2 days or so the Accord in my sig has been slow to start. I figured the first slow start was just a fluke or maybe a result of too many short trips, however each subsequent start was also slow, and getting slower. Until last night when I started it and it BARELY turned over. I drove straight home to remove the battery and head to Walmart, thankfully it was covered under the 3 year replacement deal. 
