93' 300zx coupe non-turbo 5-speed.
Recently the car behaves a little bit strange:

1) It hesitates a lot between 2000 to 2800 RPM, especially on second
and third gear. Feel like someone is playing the gas paddle. After
pass 3000 RPM everything is back to normal and powerful (again, it is
NOT a turbo version).

2) In hot summer day after the engine is shuted off for a while (half
hour to one hour), 90% the chance the "check engine" like will turn on
when restart the car. But it will turn back off after couple minutes.
It never happens in cold days.

I sent it to a local auto mechanic once and he said nothing wrong with
it according to the computer (the CheckEngine light was off). And I
cannot leave my car to him until the CheckEngine shows up again since
I need the car.

Any ideas? Are two issues related? Please help.