A BE1900 Captain experienced inadvertent aircraft movement after engine start with the parking brake set. No chocks were installed but the Captains feet were on the brakes and a fair amount of pressure was required to stop the aircraft.

Narrative

We were performing a GPU start for the #2 engine using the appropriate checklist. The parking brake was set and I had my feet on the brakes but we had no chocks installed. After I gave the remove GPU signal to the ground crew the aircraft started moving inadvertently forward. It took a fair amount of break pressure to get the aircraft stopped. The event took me somewhat by surprise; as I did not expect the aircraft to start moving at that point; especially given the strong headwind and only one engine running. I'm not sure if the cold temperatures were a factor. Nobody was hurt and no equipment was damaged but for the safety of ground agents such events must be avoided.1. Personally; in the future; I will always make sure that chocks are installed for a GPU start even if it's just for a run-up without passengers. 2. Ground agents; for their own safety; should make sure that chocks are installed for GPU starts. 3. Company should use manuals/bulletins to alert crews of the dangers of starting engines without chocks installed.