The burst current is microscopic, just enough to charge a 14pF (approx.) sampling capacitor. Suppose that charges from 0V to 2.5V, you'll need Q=CV=35pC of charge. If you take 4 samples per second that's 140pC per second, or 140pA.
The voltage divider itself will swamp that, as if you're measuring 5V with two 1M resistors you'll be drawing a steady-state current of 5/2M=2.5uA. There's not going to be any heat generated by that 
--
The Ruggeduino: compatible with Arduino UNO, 24V operation, all I/O's fused and protected