Had this problem for few years. My mechanic does not have any quick answers.
When cold (overnight) car starts fine. After driving, if I turn the car off and start it again within next 10 min or so it starts fine. If I wait longer e.g. 30 min the starter turns over fine but the car does not start right away..it takes 10-15 sec while the starter is engaged...

 

I can't say for sure, but check your ICV (idle control valve). Sometimes if it's gummed up, it will affect how your car starts, especially in situations where the temperature might vary a lot from one start to the next. You can either take out the ICV and clean it up (with brake clean), or you can replace it.

 

Couple of different possibilities. One would be a bad fuel pump check valve, allowing the fuel to drain back out of the rail and causing increased crank time. While this shouldn't be a hot/cold difference, I have seen them behave like this. You would need to check your fuel leakdown with a gauge, which can be a little difficult being the car needs to be run for awhile before this will happen.

Another option is a bad reference/speed sensor and harness back to the DME. I had a customer who was having similar issues, replaced both sensors, fuel pump check valve, and eventually it turned out to be a bad harness back to the DME, which is very common. The harness looked good, and the car never seemed to not want to start while I had my hands on it, so this was a tough one to figure out.