I posted the results of some testing I did using a little different procedure than "ccs-hello" and saw indications of spikes to 420 mA on one of my Omegas. I've pasted that post below. I second ccs-hello's comments about wire gauge and filter capacitors and would add that you want the wires short and the 3.3 V capacitor close to the Omega power pins.
Pasted post follows:
@Mark-B said in Omega2+ hot hot hot:
With my Omega2+ running on a proto-board with nothing but a linear regulator and 22 uF tantalum capacitor on 3.3 V, I got the following data points. This is monitoring current with a inexpensive USB voltmeter which has questionable accuracy at low current levels and updates about twice per second, so I'm probably not seeing the absolute peak current.
idle current ~= 110 mA
current running cpu intensive task* ~= 170 mA
current running wifi task** ~= 280 mA average, peaks around 350 mA - board is noticeably warmer to the touch, but not hot
I think this suggests that CPU activity doesn't matter much. If an Omega2 is particularly warm (and not otherwise defective) it's likely because the wifi activity is high for some reason.
* - Python for cpu task gives near 100% cpu
x = 0
for m in range(0,1000000): x = x + math.sin(random.uniform(0.0,1.0))
** - Python for wifi task run via ssh over wifi gives about 50% cpu load
for k in range(0,10000):
__ for m in range(0,k): print(m,k)
Edit to add: I see similar numbers for my Omega 2 (not plus) except "wifi" numbers are higher, with and average of about 330 and peaks up to 420 mA.
Also, the current spikes are apparent in the boot process where the serial debug suggests wifi activity with the first about 20 seconds into boot.