Agree with freethinker, probably not ignition switch.
If it does this after it gets a little warm it's probably the starter. Also likely something with the wiring. Make sure battery terminals are clean and tight, and run down the lines to make sure they haven't been spliced, cut, etc. I once had a Grand National with a warm (not even hot) start problem. Traced the wires, and someone had tried to splice in a kill switch to the solenoid, but just twisted the wires together, used smaller gauge speaker wire, etc and that was enough to make it hard to start. I eliminated the crap and it started just fine without even spending any money.
'68 GTO, 400/TH400, AC/PS/PB/PW, hideaways, Hurst dual gate
'72 442 'Vert, 350/TH350, AC/PS/PB/PW
'74 Corvette, 383/4-speed, 450 hp, restomod
'71 Javelin, 304/3-speed
'70 Cougar XR7 'Vert, 351W/FMX auto *SOLD*