Can my 1996 make it through 5 states?

It's a 1996 Ford Taurus. I don't know anything about cars. I just know mine is old. Sometimes it makes noises and if I drive for 2+ hours at a time it tends to get hot (like if I turn it off and step out, I can feel heat coming from it sort of), but it has never overheated before (the heat thing never went into the red / it never smoke). Do you think it would last driving through 5 states? (Kansas to California). What are some tips you have in order to make the journey as safe as possible if I go through with it?

You need to take it to a mechanic for a road trip service usually an oil change, fluid, breaks, and tire check. After your car has been checked out the mechanic can give you an answer about its ability to make that trip. My main concern would be climbing mountains; you might want to head south first and then head to California on Interstate 10.

Other than basic prep for long trips,
these have an inherent cooling issue never addressed by the manufacturer. The grille opening is small. Over the years working on these I've found they develop unsolvable slight to severe over heating. In some cases no real solution. Since yours is exhibiting the same issues, I wouldn't chance it.

only tip I have is to have the cooling system and all dependent systems be checked out thoroughly by a trusted mechanic.

turning wrenches since 1969.

The heat you feel is coming from the catalytic converter. If it gets real hot it means it is failing.

Sure, Kansas isn't nearly as hot as AZ. I rented a Taurus wagon in '92, drove all thru AZ and NM in April. No problem. Nice car.

I've seen worse cars make that trip, but only one way. The only way you're going to know is to try. You can have it checked by a mechanic to make sure there isn't something just about to break.