My question is would a small oil heater with a thermostat keep a 5x10 underground storm shelter above freezing say when it's 10-15 D outside at night.

If it's underground and in lower 48 it shouldn't need any heat. It would have to be -40F to freeze an underground storm shelter with a decent closed roof.

I use 2 of these in my drafty 2 car garage.  I only turn them on when temps go below 20 F outside.  I just barely put the thermostat above the frost mark.  I have temp sensors in the garage and they keep it between 35 and 40, just where I want it.  I've never tried it with just one because I didn't want the figs nearby to get hot.  In your space 1 should be plenty, even if it's drafty.

http://www.amazon.com/DeLonghi-EW7707CM-Safeheat-ComforTemp-Oil-Filled/dp/B000TGDGLU/ref=sr_1_2?ie=UTF8&qid=1446319354&sr=8-2&keywords=oil+heater+delonghi