Just installed a new starter solenoid ($13, Wells Mfg. Corp., Part No. F490 [for a '73 Mustang, 'cause the Parts Guy is gonna need to know so he can look it up in his computer]) after reading what happened to Cozman in this Forum under "Starter Problems?"
There was some green corrosion on the copper cable connections at the Solenoid. And a lot of 'dust' came off the cables with a wire brush. These cables come directly from the battery and go directly to the starter. Any corrosion will act as an insulator and not allow full passage of current. To get maximum cranking power from the starter requires maximum amperage passing freely from the battery across the solenoid to the starter motor. So, while you're checking the ground cables, you may want to brush off the Positive (+) cables at the solenoid, and for $13, put a new solenoid on, so as not to have to push start your cat at a really inconvenient time. Sometimes ya gotta check everything.
Oh yeah, mine was hesitant to start too when hot, like I had to hold the key on start for a few extra seconds before it was persuaded to start cranking over. Hope this fixes mine, 'cause it's on jack stands for another two (2) weeks for another project. If not, I'll be cleaning ground cable connections too.