Tærtens fyld er for varmt til at spise.

In Danish, for often means too / excessively when it comes before an adjective or adverb.

So:

• for varmt = too hot
• for dyrt = too expensive
• for sent = too late

That is a very common pattern, and it does not mean the English preposition for in this sentence.

Tærtens is the genitive (possessive) form, meaning the pie’s.

It comes from:

• en tærte = a pie
• tærten = the pie
• tærtens = the pie’s

Danish usually forms the genitive by adding -s to the noun phrase.

So Tærtens fyld means the pie’s filling.

After a possessive/genitive like tærtens, Danish normally uses the possessed noun in its basic/indefinite form.

So you get:

• tærtens fyld = the pie’s filling
• mandens bil = the man’s car
• husets tag = the house’s roof

Even though fyld is not marked with the definite ending -et, the whole phrase is still definite because tærtens already makes it specific.

So tærtens fyld is natural, while tærtens fyldet would be wrong.

Because fyld is a neuter noun in Danish: et fyld.

When an adjective is used after er, it still agrees with the noun in number and gender:

• en suppe er varm = a soup is hot
• et fyld er varmt = a filling is hot

So here:

• fyld → neuter singular
• therefore varmt

Til at + infinitive is a very common structure in Danish, especially after for + adjective.

So:

• for varmt til at spise = too hot to eat
• for tungt til at løfte = too heavy to lift
• for svært til at forstå = too difficult to understand

Here, at spise is the infinitive to eat, and til links it to the adjective phrase.

Because they do different jobs.

• at marks the infinitive: spise → at spise = to eat
• til is part of the fixed pattern for + adjective + til at + infinitive

So Danish says:

• for varmt til at spise

not just:

• for varmt at spise

In this structure, til is required.

Yes. The sentence means that the filling is too hot to eat it.

Just like English often says:

• too hot to eat

instead of:

• too hot to eat it

Danish can leave the object unstated when it is obvious from context. Here, the understood object is the filling.

Yes, absolutely.

That version means roughly The filling in the pie is too hot to eat.

The difference is mainly in structure:

• Tærtens fyld = the pie’s filling
• Fyldet i tærten = the filling in the pie

Both are natural. The first is a bit more compact; the second may feel a bit more explicit.

Because this is normal Danish main-clause word order:

• Tærtens fyld = subject
• er = verb
• for varmt til at spise = complement

So the pattern is simply:

subject + verb + rest

Nothing unusual is happening here.

It refers specifically to the filling, not the whole pie.

That is important because Danish has chosen fyld as the subject:

• Tærtens fyld er for varmt til at spise = the filling is too hot to eat

If you wanted to say that the whole pie is too hot, you would make tærten the subject instead:

• Tærten er for varm til at spise = the pie is too hot to eat