36V batt on 48v controller will not work if the 48V controller has a low voltage cutoff (LVC) that is too high and cannot be reprogrammed. But 48V controllers do not necessarily have LVCs like that, so you may be OK.
48V batt may burn up a 36V controller if major components (like capacitors) are not designed for it. May not happen immediately when you hook it up. But many controllers are under-rated for safety and reliability and may work fine with higher voltages.
If your battery has a BMS (battery management system) of its own, it may cause the battery to cut out too. I have encountered all three scenarios, although I am not convinced I have complete explanations for all of them.