As you may know power (mW) is heat
A couple more bits from the data sheet:
Power Dissipation (Note 6)
Molded DIP (N) 1365 mW
Note 6: The maximum junction temperature of the LM3914 is 100°C. Devices must be derated for operation at elevated temperatures. Junction to ambient thermal
resistance is 55°C/W for the molded DIP (N package).
Gluing a DIP heatsink
would help too.
You can probably do it a lot more efficiently with your arduino.
I'm not sure what you mean by efficient... A microcontroller is total overkill
when a single-simple cheaper chip will do the job.
Now, for the VU Meter "effect" I'm working on right now... It reverses, inverts (lights go off
with loudness), it has bar-graph mode, dot-mode, and dots-mode (with a random variable number of "dots"). And, it has does several other non-meter audio-driven effects. That design "needs" a microcontroller. I actually started that project a couple of years ago with an LM3914 and a bunch of other logic and shift registers, etc... It got really "messy", and I decided to "go programmable" and do all of the hard stuff in software.