Larger plug means 60 Amp or larger - most likely something of a pin and sleeve type plug, straight blade plugs pretty much don't exist above 60 amp I believe. A 100 amp version had better accept #4 conductor.
Also consider GFCI protection, potential capacitive leakage on a long run causing nuisance trips. Since this is temporary wiring it doesn't require a plug/receptacle, you can "hard wire" flexible cord in such a situation, which would also make the GFCI requirement go away.
I myself would have likely run the permanent supply conductors to the house, may or may not have installed the permanent panel depending on conditions. If not the permanent panel would have somehow installed a temp panel on those permanent conductors and made that the "construction power" and change over to permanent panel later on.