On the subject of poles - I always use two if I'm carrying a heavy pack, cos they save your knees, are, in effect, extra legs, and you can poke frisky cattle or point at interesting things with them(!). They get in the way a bit on stiles. Its difficult to predict whether or not you'd get on with a pair, though. Some people don;t like them. Could you borrow some to try them out? Or something?
As far as the temperature in summer. Hadrians Wall is a low level route , so the temperature won't be much different from the rest of England. It could be quite hot (for England) - say, 25+ degrees C. Or it could be chilly. Put the fleece in the rucksack just in case, but take the sunhat and the suncream too....