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In most situations the heat is generated by the contact resistance, so for whatever reason that connector was making poor contact. If you clean it up and properly replace the electrical connector(s), the resistance should be near zero and the heating will go away. If the corrosion is evident on both sides of the connection, changing both the male and female wire connectors would be a good idea. Increasing the current rating of that connector shouldn't be required unless there is a widespread problem indicating a design issue.
I would run the blower for a few minutes at various speeds after the repair and check that wire for abnormal heating.
An other source of heat can be from blower wire connections to large power resistors used to reduce the voltage to the blower motor, and thereby reduce the fan speed at lower settings. Wires connected directly to voltage-dropping power resistors (generally these are white ceramic packages) will have heat conducted into them from the resistor itself.
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