Why does my car struggle to turn over when warm?

I have a 96 Honda Accord ex. I just got the car and right off the bat, I had the starter changed and the ignition switch fixed. All the electrical stuff works and everything but I notice when my car starts to warm up, it struggles to start. An example of that would be if I go into the store for 5 mins and come back out/go to turn back on my car, it almost sounds like a weak battery and struggles for a few seconds but always turns on. I don't know what the problem may be, once the car gets going it runs like a champ. My breaks were checked, they were fine, my car doesn't overheat or even go over the middle line. The only problem is the struggling I sometimes hear. It makes me uncomfortable as I want to feel secure driving my car. One more add, the previous owners said they just put in a new battery but I'm wondering if maybe it isn't charging throughout the day or it is just too weak to support this car?

First, clean the battery terminals and all the ground connections. If it still does that, run a voltage test on the battery when it's hot. If it's above 12.6, then do current draw test and a voltage drop test while cranking. That'll tell you the condition of the connections.

If by; "struggles to start", you mean that it turns over but takes awhile to actually start and run, you have a bad pgmfi (main relay). They were a very common problem. You can either replace it or remove it and pull the cover off to resolder the two relays inside the box. It's up under the dash on the driver side with "MITSUBA" written on the side.

Plugged/dirty fuel filter, near dead battery and or alternator problems comes to mind