Mind if I chime in here too?
By my map, Dallas to Wichita is only 365 miles’ you’re going to drive up and down I-35/ It’s all highway miles, and will probably be before it gets really hot. This isn’t that long or hard of a drive and shouldn’t be that hard on your car.
Your Tempo isn’t really a high mileage car. Even if the engine is tired (which I question) it should make it up and back just fine. The only major things that I would worry about would be:
- the brakes (which have been checked), or
- the clutch (which you replaced, but which wore out early)
- minor things like a boilover, a flat or a broken hose or belt.
I don’t know your car, but nothing on your dad’s list seems to be specific to your car. Based on that, I assume that the car is still in fair condition.
So, that said, let me address your dad’s list:
I wouldn’t.
Someone correct me if I’m wrong, but I’m pretty sure that the Tempo’s engine doesn’t use a distributor. The only parts that will be replaced in a quickie tune up are the spark plugs. These are due for replacement if they have over 10K on them, but old spark plugs won’t leave you stranded on the road; they’ll just hurt your car’s performance (mileage, emissions) a bit.
If take your car to a regular mechanic, then I’d recommend the tune up, as (s)he will, or should, also check for any other problems. Maybe I’m just being cynical, but I have the impression that the quickie places just use their tune up as a way to drum up work that might have been part of a real tune up.
In any case, remove the air filter and make sure that you can see light through it. If you can’t, or if it looks dirty, replace it.
I would.
Didn’t they replace your hoses when they replaced the thermostat? Check them anyway. Check the belts too; if they’re cracked, replace them.
Also, carry some duct tape and hose clamps for the radiator and heater hoses. If a hose gets a small leak, you can wrap the tape around it, hose clamp it into place, refill the radiator, leave the cap latched but not tightened, and get to the next town.
(ps. You may already know this, but DO NOT remove the cap from a hot radiator; wait until the engine cools! This way, you will not get scalded when the radiator vents, and the cool water will not warp or crack the engine.)
And carry a gallon or two of distilled water. You might want it if your radiator doesn’t.
(Intermission) 
- flush out the cooling system
I wouldn’t.
If this hasn’t been done regularly before this, I wouldn’t start now. A cooling system flush uses a mild acid to remove scale. This scale can collect in the radiator and clog it, which can cause a boilover or a damaged engine. This might also rot through a weak spot in the radiator, causing a pinhole leak.
- have the brakes checked (they just were)
Hmm…
Front and back? Then just pop the cover on the reservoir and check the lever. Tell dad that they were checked. 
Your call.
I’m not a big fan of AC, so it’s your call. It might help fight driver fatigue, though. Let me add that the compressor seals can fail if you don’t use the AC for a while.
- get an oil change (it’s about that time anyways)
I would.
Like you said, it’s time anyways, and this is a good reason to do it. Personally, I wouldn’t use any oil that refers to Pennsylvania or Quakers in its name. These oils used to sludge a lot and still have bad reputations which they may or may not deserve.
I am a big fan of synthetics; they have a higher flash point (the point at which they burn), so you tend to get less coking (little bits of charcoal that used to be oil). This, in turn, leads to less engine wear. They seem to reduce friction as well.
Silo, no offense, but I am not a fan of oil additives. From what I’ve heard, neither is the auto industry, nor is Dupont, who makes the PTFE (Teflon) used in some additives. The additives in API-SF/API-SG oil are already formulated for use in turbochargers and probably can’t be improved upon by a second-source additive.
phouka, hope you don’t mind me commenting on these too:
- just passed Texas inspection
Sorry to say it, but since you’re a conscientious driver this doesn’t mean much. You already take care of the major things on your car and a bad brake light won’t leave you stranded on the road. Besides, an inspector only gets about $2.00 out of that $10.50 fee. They can’t afford to fully check your car out for that.
- clutch was rebuilt 15K ago
This worries me. It shouldn’t go out on this trip, but you should be able to get more than 75K out of a clutch.
If the clutch uses a cable, then have the adjustment checked.
I’d also recommend that you:
-Inflate your tires to the maximum pressure stated in your owners manual or on the sticker inside your door. This will increase your mileage and reduce tread wear too (the tire flexes less, so it runs cooler.) Check the spare too.
-Carry two cans of Fix-a-Flat. This way, you might be able to get to a rest station or gas station before changing the tire.
-Carry a cell phone. Normally, I hate them, but I can see how one could come in handy on a trip.
-Carry some duct tape, hose clamps and water, along a screwdriver to install the clamps, as stated above.
Above all, enjoy your trip.