48V will give 33% more torque and speed. The motor won't have any problem with that.
Some 36v controllers can handle 48v and some can't. Controllers don't cost much compared with a battery, so it's always worth upgrading at the same time.
Your 36v controller will cut off at 31V when the battery is empty. For a 48v one, it should be around 40v, so there's a danger of running your 48v battery too low. Any 36V battery charge state indicator lights you have will be on all the time because the first one goes off around 37V, which is already too low for a 48v battery.
Also, old 36v controllers have rather crude power control. When you go up to 48v, it's better to have more precise control over the additional power.
Never buy a cheap controller. It'll work, but your riding experience and control over the bike will be a lot better with a nice one, like Kunteng (KT).