I was going to suggest Bootchart but I feel like it might stop logging at login.
sshd come up well before the desktop so you might be able to SSH in from another device and run
top if you don't have
htop installed) so you can see what is nomming on the CPU.
You've got (over) 15 seconds to inspect things - so that should be enough.
If you don't have another computer/phone you can SSH in from, you might even be able to switch to a TTY (ControlAltF1) and run
htop (et al) from there while you desktop loads. It'll be harder to do but should render a similar effect.