Overheating LED lamp
What @bitsmack refers to is very common in cheap devices, also like camera flashers of olden times. Usually a non-chip resonator that converts the incoming voltage is current limited by the battery internal resistance. For 3AA in series start with trying around the 3 to 4 Ohm mark.

Do mind, though, that you should measure the current with a multimeter with the batteries and with the resistor, and try to keep within a 10% margin around fresh batteries when choosing the final resistor.

But, never exclude the possibility you accidentally used the 5V rail either. Check everything!