There's a lot to this question of why tungsten halogen bulbs last longer - while the redeposition of tungsten on the hotter (i.e. thinner) parts of the filament is one cause, it's not the only one. In fact, with some halogen bulbs it doesn't happen at all; it depends which halogen you use - I remember when they were called 'quartz iodine' lamps, and the redeposition on the filament in lamps using iodine isn't usually at the hotspots.
The other effect that I'm thinking of - which is claimed by most of the references I've read to be the only significant one, though I'd be surprised if things hadn't moved on a bit in recent years - is that the halogen bulb operates at a much higher internal pressure than a standard bulb, and this reduces the rate of evaporation of the filament. Where the halogen comes in is as follows:-
1. the bulb operates at a much higher pressure, so the envelope has to be smaller to withstand the pressure without unfeasibly thick walls.
2. Although the rate of evaporation is reduced, the internal area has reduced much more, so the bulb would become useless due to blackening of the wall from the tungsten deposit.
3. Using some halogen in the fill, combined with a high temperature at the bulb wall (which has resulted from using a small envelope) means that the halogen will combine with the tungsten on the walls, and then the compound will dissociate again, redepositing the tungste, on the even hotter filament and releasing the halogen to repeat the cycle. Unfortunately in a lot of cases it will do this before it has got to the hottest part of the filament, resulting in a thickening of other parts of the filament.
Incidentally, a lot of halogen bulbs have similar lives to standard tungsten bulbs - it's just that they'd die much faster without the halogen! The ones I use seem to have about twice or three times the life of a standard GLS bulb (the claim varies depending on which manufacturer they came from).
Going back to the original question about temperatures; there's been a lot of discussion in the UK over the years about 'long life' bulbs, which commonly last twice as long as standard bulbs - including a load of speculation along the lines of 'the manufacturers know how to make bulbs that last ten times as long, but they don't do it because they want to sell more bulbs' . In fact the standard life bulbs probably give you more light per total pound/dollar/euro expended because theire greater efficiency counterbalances the cost of buying twice as many - but there are places where actually replacing the bulb is such a pain that it's worth paying more for longer life.
In the same way the more expensive halogen bulbs give greater efficiency, and they also give a slightly different colour balance, which adds an aesthetic dimension to your choice if it's for home lighting, but could be a critical factor if you're a graphic designer!
Mike