Replace the radiator cap. Don't ask why, just try it.
You're pretty much explaining my problem, except for the fact that in mine, it happened a lot faster. The new cap fixed it. Just pop off the old, pop on the new.
Curious as to why this would make a difference? Consider the following (lol.. Bill Nye)
Water at sea level boils at approximately 100 degrees celcius. At my altitude (roughly a mile high) you'll see it boil more around 95-97 degrees celcius. Interesting phenomina eh? Wonder why it works that way? Pressure. A system under higher pressures results in an increase in boiling points for any material. A vacuum therefore results in lowered boiling points.
Why does that pertain to a cars cooling system? The radiator cap has a spring on it with a seal at the bottom. This spring is set to compress at between 8 and 20 pounds per square inch of pressure. Why is this? It increases the pressure of the system, raising the boiling point of the liquid inside, keeping it from overheating and boiling over. Just like in a pressure cooker. If this spring is "bad" and compresses at pressures like 3-8 PSI, it is easier for the coolant to boil causing an overheating situation.
You may also want to check the following- coolant plugging (not likely considering time it takes for this situation to overheat) bad water pump (can be signified by "weep holes" and is a little more likely as a decreased water flow could cause a gradual increase in temperature.
RIP 10-07- 1984 Toyota Tercel SR5 4wd Wagen 6 speed
RIP 04-05- 1986 Toyota Tercel SR5 4wd Wagen 6 speed
1st Terc- 1987 Tercel SR5 4wd Wagon 6-speed, Sadly cubed
1985 Tercel Standard 4wd Wagon w/ 3-speed auto, Living a happy life in Boulder last I knew