Must electric heaters in a warehouse/storage facility office have three-pronged grounded plugs?

There are no OSHA (or National Electric Code) regulations specific to the use of personal fans, radios, heaters, and so on in the workplace and none prohibiting their use. OSHA also does not require an equipment ground except for certain conditions.

The regulations covering equipment connected by cord-and-plug are found at 29 CFR 1910.305(g) Use of Flexible Cords and Cables. The equipment must be suitable for conditions of use and location, i.e., should not be used in areas subject to wetness and moisture unless an equipment ground (third prong) is present, not plugged into extension cords, etc. The equipment must also be approved, i.e., UL (or other official approving agency) approved which means the cord and appliance are tested together to ensure they are matched as far as current carrying and other capabilities. Other requirements to consider are in 1910.334(a) — Portable Electric Equipment.