Mom's 2001 Taurus SES has

SOUNDS TO ME LIKE FAULTY ALTERNATER AS WHEN ENGINE IS RUNNING ALTERNATER PRODUCES THE POWER NOT THE BATTERY

There have been no tune-ups in 25 years

Technically since 1980 some 32 years

Only spark plugs left from those days

The ECM,PCM in your case,or the computer
if that suits you,it does the tuning

That is a term the repair shops should stop using,
a long time ago,they have enough issues, without
misleding people.

You should have a maintenance log, for all your vehicles
You should have at least, an owner manual

Clean MAF Sensor ---every year
Brake Fluid---every 2 years
Air Filter,Cabin Filter---every 3 years
Spark Plugs,Trans Fluid, Power Steering Fluid ---every 3 years
Gas Filter--Every 3 years

Brakes--- need to come apart for inspection,rust removal & lube-every year
The System should be Scanned a couple times a year for stored data,
codes & other issues
If you look into the computer & monitor how it see things,you may avoid
problems & break down repairs

Just a few items,always something to do,have to be proactive

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either you took out the wrong bolt by the trans.... or the pin is stuck ... give it a whack with a mallet
should of taken out 2 ,13 mm bolts

1st thing you need to check is the fuses.should be under dash on the drivers side

the starter solenoid is bad. very common in the older ford vehicles. had the same problem with my 85 Crown Vic and it was the solenoid. its like a 10 dollar fix. if it sticks after you replace it then theres something wrong with your alternator backfeeding the solenoid, which is usually because it is wired wrong.

it probably has nothing to do with heat... it is probably a battery drain...need to put an ammeter inline to see if a drain... factory specs it at .05 amps draw or less.. let me know for more help

Fish engine is suplying whith hydrauliks roker arms and is very sensitive to oil temperatupe and have big oil pressure in it

Change plug wires. Most often, plug wires will only short out when they are under load, so you don't notice anything until your motor is doing a little extra work.

Hot and cold? Hmmmmmmmm, interesting,You may want to to have the air temperature sensor replaced. Its a small sensor on the intake duct coming of the air cleaner. You can change it yourself if needed. Good Luck