1993 Toyota Corolla starts for mechanic!

For the last few months, it takes between 20 to 30 seconds for the car to turn over when the engine is cold and runs rough until fully warmed up. I got a reply that it’s the fuel pump. I took it to the garage on Wednesday night, but when they tried to start it on Thursday morning in their unheated garage, it started right up! Is there some minor adjustment that could have been made to make it all better? I left it there another night and will find out today what’s going on. But any ideas? Is this something that could heal itself in their garage, but not mine?

There is nothing to “adjust” - other than perhaps the contents of the fuel filter - i.e. as in replace it.

This mechanic needs to investigate the fuel delivery system - put a fuel pressure gauge on it, leave it on, see what happens after it sits overnight, check the operation of the fuel injectors etc.

The other thing to look at, check, and perhaps clean is the idle air control (IAC) valve.