Amber light = bad
Red light = really bad
Flashing red light = you're going to destroy your engine if you continue to drive it.
How is the coolant level in the radiator? (Make sure it's cooled down before you take the cap off)
Coolant level in the reservoir bottle?
Any coolant leaks, wet spots underneath? Coolant smell/odor?
Is there heat available from your vents inside if you turn the HVAC control to hot?
Pull out the oil dipstick ... How does that look? Normal?
Visually check the water pump belt (there is a separate belt for the water pump itself)
I noticed you said you recently had the water pump replaced. Did you have the flashing red temperature warning light before and that's why you had the water pump replaced?