Hendes øre bliver varmt under huen, når hun cykler hurtigt.

Because sit is only used when the owner is also the grammatical subject of the same clause.

In Hendes øre bliver varmt ..., the grammatical subject is øre (ear), not hun (she). So Danish uses the non-reflexive possessive hendes.

Compare:

• Hun vasker sit øre. = She washes her own ear.
  
  • Here, hun is the subject, so sit works.
• Hendes øre bliver varmt. = Her ear gets warm.
  
  • Here, øre is the subject, so hendes is needed.

Also note that it would be sit øre, not sin øre, because øre is a neuter noun.

Because hendes already functions as the determiner, just like her in English.

So Danish says:

• hendes øre = her ear

not

• hendes et øre

This works the same way with other possessives:

• min bog = my book
• deres bil = their car

The sentence is talking about one ear, not both ears.

Danish often uses the singular for body parts when only one is meant or when the speaker is focusing on one specific part of the body. So hendes øre simply means her ear.

If both ears were meant, you would say:

• Hendes ører bliver varme ... = Her ears get warm ...

Because øre is a neuter noun: et øre.

In Danish, adjectives agree with the noun they describe. With a singular neuter noun, the adjective usually gets -t:

• en varm hånd = a warm hand
• et varmt øre = a warm ear

The same agreement happens when the adjective comes after bliver:

• Øret bliver varmt. = The ear gets warm.

So varmt matches et øre.

Bliver means becomes / gets, while er means is.

So:

• Hendes øre bliver varmt = Her ear gets warm / becomes warm
• Hendes øre er varmt = Her ear is warm

The sentence is describing a change of state while she is cycling, so bliver is the natural choice.

Huen is the definite singular form of en hue.

• en hue = a hat / cap / beanie
• huen = the hat / the cap / the beanie

Here, the sentence means the specific hat she is wearing, so Danish naturally uses the definite form:

• under huen = under the hat / under her hat

Danish often uses the definite form when the object is understood from the situation.

Because the ear is physically beneath the hat. Danish commonly uses under with clothing or something covering part of the body.

So under huen is very natural for under the hat / under her hat.

Depending on context, Danish can sometimes use other prepositions with clothing, but in this sentence under is the standard, idiomatic choice.

Når is used for something that happens whenever, when, or as a repeated/general situation.

So:

• når hun cykler hurtigt = when/whenever she cycles fast

This sounds like a general fact or a repeated situation.

Da is usually used for one specific event in the past:

• Da hun cyklede hurtigt, blev hendes øre varmt. = When she was cycling fast, her ear got warm.

So in your sentence, når is correct because it describes a regular or general situation.

Because after a subordinating conjunction like når, Danish uses subordinate clause word order.

That means the basic order is:

• conjunction + subject + verb

So:

• når hun cykler hurtigt

not

• når cykler hun hurtigt

The second pattern would break normal Danish subordinate-clause structure.

This is different from main clauses, where Danish often has verb-second word order:

• Hun cykler hurtigt.
• I dag cykler hun hurtigt.

But after når, the subject comes before the verb.

Here hurtigt is an adverb, meaning quickly / fast. It describes the verb cykler.

Many Danish adjectives form an adverb by adding -t:

• hurtig = quick, fast
• hurtigt = quickly, fast

So:

• en hurtig cyklist = a fast cyclist
• hun cykler hurtigt = she cycles fast

Even though the form looks like the neuter adjective form, here it is functioning as an adverb.

Because the sentence describes a general or habitual situation.

• hun cykler hurtigt = she cycles fast / she is cycling fast

In Danish, the present tense is often used for:

• general truths
• habits
• situations that happen repeatedly
• situations described as currently happening, depending on context

So cykler fits well with når, which often introduces a general when/whenever clause.

Øre contains the Danish vowel ø, which does not exist in standard English.

A rough guide:

• ø is somewhat like the vowel in French deux or German schön
• øre is roughly two syllables: Ø-re

The r in Danish is usually softer than in English, and the final e is a light vowel sound, not a strong ee.

A very rough English-friendly approximation might be something like UR-eh, but that is only approximate. The exact Danish sound is more rounded.

Sometimes yes, but it changes the style and structure.

• hendes øre explicitly says her ear
• øret means the ear

In Danish, body parts are sometimes expressed with the definite form when ownership is obvious from context, especially with verbs involving the body. But in this sentence, hendes øre is clear and completely natural because it directly identifies whose ear it is.

So hendes øre bliver varmt ... is a very normal choice.