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Earbud use can cause your ears to get uncomfortably warm inside. Having a cooling airflow through your ears could help, but a fan would be tough to make small enough and might consume too much power.
An alternative to a fan is a microblower , which uses an oscillating part and a passage shaped
to provide a directional bias to the flow (instead of the one-way valves used in a diaphragm pump), but those are not widely available. Hold onthere's already an oscillating part in earbuds: the speaker!
So we just need to provide unidirectional airflow paths in and out of the earbud, with the inward path passing through the speaker and the outward path passing by it. These passages can incorporate Tesla valves  to provide the one-way valve function. The Tesla valves can be coiled up (such as ) to fit a greater length (and therefore higher valve performance) into the space constraints of the earbud.
The outward passage also needs to provide some resistance to outward flow at audio frequencies, though also less resistance to outward flow at DC than it does to inward flow (i.e. a low-pass or DC-pass filter), so that the speaker can produce temporary pressure changes inside the ear canal, to be perceived as sound. This can be done using just the momentum of the air in the passage if it's long enough (using the passage as an inerter ), or by putting a porous membrane of some sort across the passage.
Thereby, the normal AC sound waveform coming into the earbuds from the audio source is used to produce a DC-component-having airflow through the ear, which can carry away heat and moisture.
By using the speaker as the blower, there is also no need for additional power to be supplied to the earbuds, so they can use the standard headphone connector (if wired).
 Murata microblower
Mentioned idea body. A device to generate airflow by an oscillating piezo element and a passage that provides a directional bias to the flow without one-way valves. [notexactly, Mar 15 2020]
 Wikipedia: Tesla valve (aka valvular conduit)
Mentioned in idea body. A shaped passage that acts as a one-way valve with no moving parts. [notexactly, Mar 15 2020]
 Thingiverse: Coiled Tesla valve
Mentioned in idea body. See pictures 3 & 4 for cross-sections. Unlike this one, I would try to design a coiled Tesla valve with all of its loops going outward, because that seems like it would be more compact. [notexactly, Mar 15 2020]
 Google: fluid inerter
Mentioned in idea body. There isn't one canonical reference page on these that I could find. It's basically like an inductor, but for fluid flow instead of electric current. Confusingly, mechanical inerters (though maybe not also fluid inerters) are said to correspond to electrical capacitors and mechanical springs to electrical inductors, which seems backward to me. [notexactly, Mar 15 2020]
 idea: Thermosiphon Central Heating
Thermosiphon Central Heating
by [bs0u0155]. Mentioned in idea body. We discussed fluid inerters there in the past. [notexactly, Mar 15 2020]
||Sounds like a miniature Auxetophone. Problems would include sound leakage outwards, potentially deafening other members of the public within viral contagion distance, and (less likely) sound from outside leaking in and spoiling your listening enjoyment.
||Those (compressed-air amplifiers) modulate DC airflow to add an AC component to it. This rectifies an AC airflow to add a DC component to it. Power (AC + DC) is limited to that of the speaker (as in regular earbuds), and sound is contained by the low-pass filter on the output passage.
||However, your mention of that, and my reading about it again, has inspired some more compressed-air amplifier-related ideas
||Don't restrict this to earbuds however, I find the heat much
more of a problem in the very excellent over-the ear full
size types that I'm currently wearing. You might also want to
add sub-micron filtration, ear gunk and complex enclosed
galleries are a bacterial dream. You could also use
copper/silver as an inhibitory surface.