I was going up steep hill and it shut off. Won't go on at all.

No
not if you drive it accordingly
steep hills are best negotiated in low fears with plenty of rpm applied
for example on a steep grade with a manual 1st or 2nd or possibly 3rd and the rpm around 2000 constant will cause it no harm
automatics will go to first automatically so keep the rpm at that mark
engine damage is experienced when the gear selected is too high and the engine is placed under extreme load so down shift to allow the engine to work easily
When going down hill select first and only use the brakes to maintain the 2000 rpm range and allow the engine compression to hold the car speed back
the rule of thumb for experienced drivers is this
you select the same gear to go down that it took to come up

It will lack lots of power going up hill, especially if its a really steep one and you keep it in drive. Make sure you downshift to second, or fist if its really steep.

if its not going int o red zone it is normal to get hotter as she climbs hills

sounds like a fuel issue how are the rmp's when going up is the vehicle starving for fuel may be a restriction in fuel system

how steep of a hill was it?steep enough for oil to go forward into the from of the engine roll it to a flat surface and check the oil level if ok run the engine and let it burn off if the hill ii's that steep then stop using it on the hill check the manual for running angles

could be getting an air lock in the fuel line somewhere

either your drive belt is loose/stretched or your transmission is going out. check the belt and tensioner.

going down steep hills will all but over ride a cruise control, since the motor is trying to keep the vehicle slowed to what your desired speed that you set , unfortunately this doesn't always work,, as your speed increases, the motor can't keep the speed reduced, when you apply the brakes, the system shuts off, cruise controls were meant to be used pretty much on long flat surfaces with Low inclines ,,

the batteries could be the problem, is it possible to try some other batteries, silly question , how steep is this hill ? remember scooters cannot climb steep hills as the motor will shut down due to the increased load.

1 Year old batteries ok ? but if they get used on a non daily basis and are not fully charged after use, I would question the batteries but again the motor could be overloading,

How much do you weight ? sorry for the personal question but it all loads the motor and that increases the current and that will cause the motor controller to shut it down.

shift your gear to the left one tap to go into drive 1 when climbing steep hills and it keeps you from hesitating .it works for me i have a 2009 caliber automatic and i climb alot of kentucky hills ,mine only hesitates on the really steep hills after i slow down and take off again but when i shift to d1 its fine