Does food cool down quicker when heated up via a microwave than when
it has been cooked the 'normal' way (in boiling water).

I have often heard people say that microwaved food cools more quickly,
but scientists say otherwise. Food that has been cooked in a microwave
oven may seem to cool down sooner than food cooked in a conventional
way, but the inside of a microwaved food item can be very hot even
when the surface is cool to the touch.

"You want a nice, hot meal but you're pressed for time. So you pop the
food into the microwave and - presto - it's ready to eat in seconds.
But then the food seems to cool so quickly. Don't blame the microwave.
Research from Penn State University finds meals cooked in a microwave
oven stay hot longer because they cook from the inside out. The food
only seems to cool faster because heat dissipates from the surface.
Inside, your food is still hot."

KITV: The microwave vs. the stove
http://kitv-tvhealth.ip2m.com/index.cfm?PageType=itemDetail&Item_ID=11716&Site_Cat_ID=13

"Do meals cooked in a microwave cool faster than those cooked conventionally?

Actually, microwaved meals stay hot longer,' [food scientist]
Anantheswaran Anantheswaran says. 'Microwaves cook from the inside
out. As heat on the outside dissipates, the food seems cooler. In
reality, it is hotter on the inside. The principle is seen easily by
heating a jelly doughnut: the outside is relatively cool, whereas the
filling may be scalding hot."

Penn State University: A Food Scientist's Microwave Top Ten List
http://aginfo.psu.edu/psa/fw98/food.html

"When two identical items are cooked, one with a microwave oven and
the other on the stove, which will cool faster? -- CR

If the distributions of temperatures inside the items were the same
after cooking, they would cool at the same rate. However, a microwave
oven tends to cook relatively evenly throughout the food while the
stove tends to cook from the outside of the food inward. That means
that food cooked in a microwave oven tends to have more thermal energy
near its center than food cooked on a stove, even when those foods
contain the same total amount of thermal energy. Since foods lose heat
through their surfaces, the extra thermal energy in the food cook by
microwave will take longer to flow out to the surface of the food and
from there to its surroundings. All else being equal, I would expect
the food cooked in the microwave oven to cool slightly slower than the
food cooked on the stovetop."

How Things Work: Microwave Ovens
http://howthingswork.virginia.edu/microwave_ovens.html

My Google search strategy:

Google Web Search: microwave OR microwaved "cool OR cools faster"
://www.google.com/search?hl=en&q=microwave+OR+microwaved++%22cool+OR+cools+faster

Google Web Search: microwave OR microwaved "cool OR cools more quickly"
://www.google.com/search?hl=en&q=microwave+OR+microwaved+%22cool+OR+cools+more+quickly%22

I hope this information is helpful. If anything is unclear or
incomplete, please request clarification; I'll be glad to offer
further assistance before you rate my answer.

Best regards,
pinkfreud