DIAGNOSIS The warming plate doesn't have a variable thermostat; it's a simple heating element that runs at a fixed, fairly high temperature. It's designed to keep a full carafe hot, not a single cup.
FIX There's no setting to change the temperature. The workaround is to pour the remaining coffee into a thermal carafe or insulated mug as soon as it's done brewing. Don't leave a small amount sitting on the hot plate for more than 20-30 minutes.
IF THAT DIDN'T WORK If the plate seems excessively hot even with a full carafe (scorching, not just warming), the thermal sensor next to the plate might be faulty, but this is less common.
HEADS UP That borosilicate carafe is tough against thermal shock, but constant direct high heat on a small amount of liquid will cook it and stain the glass. It's a design limitation of most simple drip makers.