Engine misfire when hot

G'day. I could really use some advice about a problem I've had for a couple of weeks. I have a 2017 Jimny, automatic. When I start the engine cold, everything works fine. However when I stop it, let it cool down for a few minutes and restart it, it's getting a constant misfire. The engine shakes like crazy, revs are very low (almost to the point of stalling) and the car has no power, it can barely accelerate to 30 kph. I try not to drive it in such state, but was forced to a few times and after driving like that for long enough - it just goes away. There are two other things, possibly related to the issue. Sometimes, even when working normally, when I try accelerate form stationary (e.g. at an intersection), the revs drop to almost stalling for half a second and then the car drives normally again. The other thing is that I think I sometimes hear a faint rattling from the back of the car when accelerating.

I did some basic research online and the symptoms are similar to what people write about a faulty fuel pump. My local mechanic however says that simple things like a fuel pump or an ignition coil either work or not and can't just work sometimes. He also said that a faulty oxygen probe would be recorded in the error log and the whole ting this is probably a computer issue. Which seems weird because there is a clear correlation with temperature, it only happens on a hot or warm engine. Why would a computer fault rely on temperature? Anyway, the mechanic told me to go to the Suzuki dealer because they have better diagnostic tools.

Now my question to the community: does that make sense? The dealer will charge me $400 for just looking at it so I'm seeking an advice here first. Does anyone have similar experiences? What could be causing such problems?

One of those sensors, or a coil pack.  The sensors are generally cheap enough to swap and see if that solves the problem.  Original Suzuki coil packs are not cheap but you could try a pair of used ones (search for packs from an M13A engine, which includes other models like the Swift, and avoids the Jimny price premium).

Sounds very similar to mine and it was the crank shaft sensor as lambert mentioned. If you do try replacing it just be careful not to over tighten and snap the bolt