cars dont like starts in "blazing heat". The engine under the hood get really hot and when you start it, the hot air gets in and it has really low density. So the ECU is adding more fuel into the mixture trying to compensate. But the operational temperature of the engine (coolant and oil) is low, so the ECU is adding even more fuel into the mixture. I bet your exhaust in that moment must smell after gasoline a lot. The result is very rich fuel mixture and the engine doesnt take it very well and is going rough. After few minutes of driving, the inlet air cools down and the operational temperatures of the fluids go up, the ECU stops to compensate - everything evens out.

All and all - its normal behaviour in extreme conditions.

Try to avoid parking your car in direct sunlight, try to find at least some shade. It can help a little. Anyway - its not that serious, just drive the few first miles slow, do not rev the engine much.

And change the oil dammit!

If your 6000 over on your oil change I have a feeling you don't maintain the car anywhere else either. Its been neglected. That being said, there's probable a small list of repairs it has needed for awhile, and now this one. Take it in, and maintain it correctly from then on. Those cars/any cars properly maintained should easily go 200,000 mi.

The check engine light came on good news take it to auto zone or Orielys and let them do a diagnostic on it. Or any automotive part store that offer that for free in your area

If i had to guess i bet its just the plugs or the wires or both since you haven't done a tune up on her. I had this happend on my ford t-bird before i learned the basics and my mazda when i bought bad wires and returned them and issues is allways fixed. Its a easy job but if your unsure be sure to have a buddy help with you repair your dont want to mess up on this one for sure

I think you need to worry about YOU. You are abusing this vehicle. No wonder is is falling apart. Please, sell this car immediately. You have no sense of ownership and apparently you do not have $30 bucks for an oil change but money for a a vacation? Yeah. Sell it.

why

I have a 2000 Ford Focus SE with roughly 126K miles. It's a great car, but I've been noticing some issues,

So when I went on vacation for a week, the car sat in the blazing heat without being driven, so when I got back, of course when I started driving it, it was jerky and the engine would stutter or "hiccup", but as I drove it for about 5 minutes, the car went right back to normal.

This has been happening every time I let it sit in the heat.

But that's not the problem, just earlier when I left work, the car did the normal jerky feeling when I started it from sitting too long, but this time it died completely and it gave me the check engine. When I turned the car back on, this time it was REALLY weird; the car sounded like it was going up and down, it was like it was dying but trying to stay awake. The lights would get dim and then be bright again. And of course when I drove it for 5 minutes, boom back to normal.

Is this even normal for my car? Is it something serious?

The only thing I can think of that might be causing this is it needing an oil change. I'm 6,000 miles past my next oil change (Couldn't find time and maybe a little procrastination).

I don't know, I'm no mechanic so I was just wondering if it's an oil change that could fix it, or is it something more serious?