Which is cheapest route?

To the OP. I would diagnose whatever is wrong with your car that it is getting hot before undertaking a cross country trip. A radiator should be around 100 bucks new, water pump 30ish, hoses 50 ish. All parts much less if you source used from a junkyard. Watch youtube for instructions how to change it all out, its easy. Changing out a head gasket isnt even all that difficult. I know you are doing your best to move cheap. But tows or overheated/blown motors are not cheap.

Do not take 17 south from flag if you are afraid of abrupt elevation change. Yes it is technically down hill, but there are some good up hills also.

40 from flag to Kingman has lots of downhill but some good uphill elevation change. to get around the mountain climbs take rt 66 from seligman to kingman (train runs this route, it is much flatter)

The needles grade in california can be partially avoided by taking hwy 95 north to goffs rd (rt 66 along the rail road again) back to I 40 or run 66 all the way to Ludlow ... it is a lonely road if you break down though.

I do not really see the 15 as deep in LA traffic. The 215 is even less so.

I 10 across Texas, NM, Az, and Cali are going to be a scorcher for you and your car if it is having issues.

As to the comment about TAP diesel. I dont know what that is, unless you are trying to be funny about tapping others tanks and stealing fuel. I do not notice too much of a mpg difference between "good" diesel vs ####ty biodiesel. I drive a brick pulling a parachute. Wind is more of a factor than anything else. I just know that if I get fuel at TA, Petro, Little America, or some mom and pop that uses a name brand my truck runs smooth enough I can write my log on the steering wheel with the truck running. If I put the loves bio diesel garbage in my tank, I wouldnt be able to stay in the lines on a coloring book it shakes so bad while idling.

 

I-17 southbound from Flagstaff has an 8° sustained climb. Not a good option for overheating issues.

Either 59 to 10, or the 40 to 30 to 20 to 10 to CA-60 to catch I-215 south to I-15 and Temecula. Run Dallas/FW at night if you can help it.

If you run Phoenix during the day and I-10 traffic is backed up with rush hour, take I-8 west then AZ-85 north to I-10 to bypass Phoenix. You also have an option to bypass El Paso in rush hour, the TX-375 loop (very scenic and steep).

 

If you are going to run with the heat on and windows down, if I were you I would run at night the whole way and grab a motel to sleep.

By the way, I will be flying out there next week to get some R&R.