Are the controller components rated to work at higher voltage? This would primarily be the electrolytic capacitors, which are usually rated for either 50V or 63V. If only 50V, they will eventually blow up if run on 48V. How do you know? You look at them. All of them.
Is there an over-voltage circuit? Well, you can't tell until you hook it up. If it runs, there isn't one.
There is always a low voltage circuit, set around 30 V for a 36V battery. A 48V battery cannot be allowed to run that low, but most of them have their own low voltage shutoff.
Your battery indicator will be wrong, if you have one.
And keep your second controller ready. You never know if the circuit has something else in it that will pop at higher voltage.
I have several batteries that are 36V, 48V, and 52V, and I like the flexibility of being able to put any of them into my ebikes, but I only do it if I believe the controller is compatible. I cannot run my 48V middrive motor on 36V though. It won't start because it thinks the voltage is too low. I had one controller where the capacitors were only rated for 50V. Too bad, as it was very nice. I swapped it out for a higher voltage model.