All else being equal, no, of course not. Two bodies of equal mass and composition at the same temperature will both cool down at the same rate, regardless of whether they were microwaved or oven-baked.
But of course, all else is never equal. A cake baked for 1 hour at 350 degrees is not the same as a cake baked for six hours at 500 degrees, and then allowed to cool, and then heated back up to 350, even though both are at the same temperature. There will be all kinds of differences in how much moistures is in those cakes even though they’re at the same temperature. So that would result in one of the two having more mass than the other, which would slow down how fast it cools. Same thing with the microwave – it’ll have more/less moisture than the over-baked food, and that will affect cooling time.
A microwave operates by agitation of molecules in the substance thats in the device. As it happens, microwaves have an easier time with moist things, and a harder time heating up dry things.
In addition to this, they may or may not have cool and/or hot spots. And the device may or may not have something to rectivy this (commonly a spinning plate).
I agree that all else being equal, they would cool down the same.
However, this is rarely – if ever – the case. I think that a microwaved dish can stay hot longer than an oven baked partner if the object in question is moist, and the cooking time is short. This could leave the oven baked partner only having the outside heated, and the inside very cold(though I’m sure the same can be said about microwaves) .
Conversly, an oven cooked object which has been heated over a long exposure time and is dry may have not heated the object in a similar amount of time.
Note: This is mostly conjecture, and I do not have cites readily available for what I remember reading. Take this with at least a grain of salt, if not a silo.
In my experience, foods cooked in a microwave don’t cool down appreciably faster that foods cooked any other way. For example, I boiled rice in the microwave last night and it was hot to the last bite. However, foods re-heated in a microwave seem to cool down quicker, probably for all or more of the reasons already mentioned.