Inflammation in feet causes redness pain increased temperature after walking or standing short periods, what is the biological process that takes place like what is happening?

The classic signs of inflammation are swelling, redness, heat, pain and lose of function. All caused by substances released at the site by wbcs responding to the injury/infection. The arteries vasodilate = swelling, redness , warmth. Pain & lose of functions are related to chemicals release that stimulate pain receptors. Check Wikipedia for more details. Standing pools blood in feet=redness.

Firstly do you wear ill fitting footwear? Is it simple fatigue of the feet or an uncommon condition called erythromelalgia? A podiatrist, preferably at a department of podiatry, at a university hospital near you, would be worthwhile consulting.