It would care because the starter is drawing more current when it's hot and the ignition circuit is not providing it. You can find pictures in her of people who have wired in a Ford starter solenoid near the battery to solve this problem. You can also find a thread with a description of cleaning the electrical contacts inside the ignition switch which also solved the problem.

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13