86 560 SEL Cooling system question

Noticed something the other day with car running and sitting in park for about 15 minutes. Temp went up to 110 C and aux fan kicked in bit temp continued to stay at about 110-115. Reving the motor immediately brought down the temp. Heat from climate control was warm, but not scorching hot at idle but when rpms picked up heat was hotter. After starting to drive again, temp stayed at 85 C even after I stopped with car running for about 5 minutes. Radiator, fan clutch and T-stat are new. Temp outside was about 45 F. So this problem does not always occur. What are the symptoms of a defective aux water pump and can a bad one cause engine temp to rise significantly? After reving the motor a few times the heat inside the car stayed hot. Any ideas?