Owner of a Thinkpad X1 3rd gen running Debian (started with Jessie, now Stretch), and my experience is quite different but there are some things to know. Let's trade anecdotes:
> - Wifi is flaky (ier than on windows)
No problem there, always been rock solid. The chipset is likely to matter, my laptop uses an Intel chipset. Performance wise Intel may not be the best, but the Linux support has always been good in my experience.
> - Battery life is shit (ier than on windows)
A very common misunderstanding, and very easy to solve. The thing is, a stock Linux distro is made independently of the PC hardware that will run it. There's no integration like any PC vendor does when installing Windows, making sure the Windows configuration is well tuned. In order to be functional on most devices, a Linux distro is typically conservative, and will typically stay away from enabling low-power modes that are flaky on some crappy PC models.
But for most tier 1 PC brands, the hardware is fine and it's perfectly safe to enable aggressive low-power. So just install a package like The Laptop Project (tlp), or the older laptop-mode, and you're good to go. You can even tune the configuration, it's simple and well commented. For example, with a fast SSD (no spin up/down), one can be very aggressive on putting the drive into low-power.
With this done, taking about 10 mn tops, I have a longer battery life on Linux as on the stock Windows8.1. And this is as reported by the firmware through ACPI, so same estimator on both sides.
> [Various sleep mode issues]
There was a very nasty bug in Linux MMU set-up that's been solved in 4.8. Before this, it could trigger some random and sometimes hard to reproduce bugs on some models, leading to crashes on resume. I've been affected, and it was a pain. The bug was there for a long time apparently.
Since 4.8, it's been rock solid. Zero issues. And it's really night and day in term of user experience. In case some of your issues were related, you may want to make sure you're running a recent enough kernel.
As for the unwanted wake-ups in a bag turned into an oven? Only ever happened to me on my work TP running Win7. From experience, sleep is not perfect there too.
No experience on using an external monitor with my Linux laptop.
One of the main weakness is that there's no ODM integration if you install Linux yourself. With big brands like TP, it's still mostly been smooth in my experience, except for the nasty resume bug fixed in 4.8. If that's a problem for you, there are now vendors with pre-installed Linux. Then it's a similar situation to Windows.