Hmm maybe this should be in the homework section.
1 - the body's thermoregulation (homeostasis is the topic you'd start with) system dilates
"local" blood vessels near the skin when the body's core temperture rises due to high ambient temperature, exercise, or sometimes illness. The trigger is the level of intracellular calcium and phosphorylation of mysosin (MLC mysosin light chain molecule).
2. Your core temperature (the warmest blood) varies in a diurnal rhythm and across individuals and physical exertion levels and age. Withe regard to age: Brand new newborn infants do not thermoregulate the way us big people do. You have to keep them warm and dry for several hours, and not let peripeheral blood temps go below guidelines. For example, nurses will defer bathing until the baby's axillary temperature is stable and above 36.4 deg C, and keep the baby's head covered with a cap minimally for the first twelve hours.
Peripheral blood tempatures can vary even more due to environmental factors.
Temperature readings on one person measured at the same time at different places also vary. Temperature (the 98.6 deg F you probably know as "normal", or oral temperature) will be slightly higher when taken rectally or taken from the tympanic membrane - about 0.5 deg F to 1.0 deg F higher. Axillary temp (armpit) will be lower.
So there isn't a one 'temperature'. And I don't think glycolysis per se is a massive contributor, because I've read that consumption of oxygen correlates well with core temperature readings - the basic metabolic rate - and glycolysis is anaerobic.
One digression - there is a hypothesis that one contributor to obesity in developed nations is central AC and heat. Because the body does not spend a lot of extra calories cooling off or staying warm. You decide if you like this idea. I find it interesting.