Toughest bits for heat and hills will be approaching kielder and leaving robin hood's bay.
Not many of the control towns have 24 hour facilities as far as I can tell so going nocturnal to avoid the heat is not an option.
I'd add the NYM Eskdale roller coaster from Kildale across to where you join the A171.
Stanhope(323) ATM 3 doors down from Coop
(Parkhead Station cafe opens at 9am Saturday - recommended, and they know some may stop there) It's 4km and 235m up Crawleyside, above Stanhope. Food there in 2016 was a darn sight faster than the cafe in Stanhope. They cook to order.
Kielder(417) - if you're not going to make Kielder by 1700 (village shop closing time) then . . . 'Kielder' Tower Knowe Visitor Centre is 13km earlier, on the right, overlooking Kielder Water (well signed and has cafe - closes at 5pm)
Lockerbie(480) ATM and see Andy's info
Penrith(550) ATMs. Shell Garage is open 24 hours (on the A6 road going south after the centre of town)
Yarm(692) 24 hour garage
Robin Hood's Bay(755) ATM down in village - Fish Box closes at 6pm on Sunday (NB 260k to go)
Ripon(853) 24 hour garage
As an aside, in 2016, two of us ended up in the 'Cross Keys' in Canonbie (01387 371010, 40km from Kielder). Excellent food, fantastic beds and the best 11 hours sleep I've had this century.