in theory maybe, but the practical difference would be tiny.

the hotter CPU will still produce the same about of heat energy.  the only question is how well is this heat dissipated.

For some reason I thought that a badly-cooled cpu consumed more power so the heat pipe worried me

not sure what the heat pipe has to do with the battery life.  if it is overheating it will throttle the CPU power or power off.

what are the temperatures.  that is what really matters.

Nothing wrong, will still work as it should and it's not related to the battery life at all.

Laptops never get thier nominal run time unless you are looking at a blank screen with 25% brightness. As for Linux make sure you have TLP installed it still won't be as good as windows but it will be better. My t480s is worse battery in Linux. But my t420s has better battery under Linux both with TLP. Some work better.

I don't know about Linux, but on Windows it will boost the processor aggressively regardless of power source.  If you were to turn that off or throttle down the processor it might give you better battery life.

If there is big temperature difference on the heatpipe between before the bend and after the bend, then it's really damaged and should be replaced. 

Anyway if the CPU senses that it is too hot it will reduce its clock freq.
The performance and the consumption will be low then.

The temps on the insides of the tubes whether bent or straight has the same variation. Just think as pressure of water in an aquarium is equal to all sides the water is touching.. I am using auto-cpufreq and it works fine on my x220 and x201

Eh. Performance will be slightly degraded by the restriction in the pipe but if it were me I would just use it until it catches fire like all the other hardware I own.

Linux battery life is just trash sometimes. Try auto cpu freq

Slightly bent vent tube, is it serious? With my hands I don't feel any heat from my CPU when using Linux, but I still get 1.5hrs of battery lifetime, could this be the cause?