Vi undersøker hvorvidt lagerboden er frostfri eller temperert.

Hvorvidt means whether.

So Vi undersøker hvorvidt ... means We are checking/investigating whether ...

A very important grammar point is that hvorvidt introduces an embedded clause, not a direct question. That is why Norwegian uses normal subordinate-clause word order:

• hvorvidt lagerboden er frostfri
• literally: whether the storage shed is frost-free

You would not say hvorvidt er lagerboden ... here.

Also, hvorvidt is a bit more formal or written-sounding than om.

Yes. In everyday Norwegian, om is often more common.

So this would also be natural:

• Vi undersøker om lagerboden er frostfri eller temperert.

Both mean essentially the same thing here.

A useful rule of thumb:

• om = common, everyday whether/if
• hvorvidt = more formal, often used in writing, reports, official language, or careful speech

In this sentence, hvorvidt makes the tone sound a little more formal or technical.

Because Norwegian very often forms compound nouns as a single word.

Here you have:

• lager = storage / stock / warehouse-related
• bod = shed, stall, small storage room, closet-like storage space
• lagerbod = storage shed / storage room
• lagerboden = the storage shed / storage room

The -en at the end is the definite ending for a common-gender noun.

So:

• en lagerbod = a storage shed
• lagerboden = the storage shed

This is very typical in Norwegian. English often separates these words, but Norwegian usually joins them.

Because after hvorvidt, you have a subordinate clause, and subordinate clauses in Norwegian normally use subject + verb order.

So:

• hvorvidt lagerboden er frostfri
• subject = lagerboden
• verb = er

Compare this with a direct yes/no question:

• Er lagerboden frostfri? = Is the storage shed frost-free?

So the difference is:

• Direct question: Er lagerboden ... ?
• Embedded question/subordinate clause: hvorvidt lagerboden er ...

This is one of the most important word-order differences in Norwegian.

Undersøker is the present tense of å undersøke.

• å undersøke = to investigate, examine, check
• vi undersøker = we investigate / we are checking / we examine

In this sentence, undersøker can sound a bit more formal than just sjekker, but both may work depending on context.

For example:

• Vi undersøker ... = We are investigating/checking ...
• Vi sjekker ... = We are checking ...

Undersøker can suggest a slightly more careful or systematic check.

Frostfri literally means frost-free.

It is made up of:

• frost = frost
• fri = free

So frostfri describes something that does not go below freezing, or is protected from frost.

In practical terms, for a room, shed, or storage area, it means the temperature stays high enough that frost does not form and contents are protected from freezing.

This word is very common in contexts like:

• storage rooms
• pipes
• freezers/appliances
• greenhouses
• building descriptions

No, not in the English metal/glass tempered sense.

Here temperert means something like:

• kept at a moderate temperature
• temperature-controlled
• sometimes lightly heated

In building or storage contexts, temperert usually means the space is not fully cold/unheated, but also not necessarily as warm as a normal living room.

So in this sentence:

• frostfri = above freezing
• temperert = kept at a moderate, controlled temperature

Depending on context, temperert may imply a somewhat warmer or more controlled condition than just frostfri.

Because the subject is lagerboden, which is a common-gender singular noun.

In Norwegian, predicative adjectives often agree with the noun:

• common gender singular: base form
• neuter singular: often -t
• plural: often -e

So:

• lagerboden er frostfri
  common gender singular

Compare:

• rommet er frostfritt
  neuter singular

• bodene er frostfrie
  plural

The same principle applies to many adjectives, though temperert already ends in -t, so its form does not visibly change here.

Because frostfri and temperert are adjectives used after the verb er. They are describing the subject, not functioning as nouns.

This is called predicative use of an adjective.

So Norwegian says:

• Lagerboden er frostfri.
• Lagerboden er temperert.

Not:

• Lagerboden er en frostfri
• Lagerboden er en temperert

Those would be wrong, because the sentence is saying what kind of condition the storage shed is in, not naming it as a thing.

Yes, eller means or.

Here it links two possible conditions being checked:

• frostfri
• temperert

So the sentence is saying that they are checking whether the storage shed is frost-free or temperature-controlled/moderately heated.

After hvorvidt, it works much like English whether ... or ...

The sentence does not necessarily force a strict logical distinction in everyday use; it simply presents the relevant alternatives under consideration.

It is natural Norwegian, but it sounds a little formal or practical/technical, mainly because of:

• undersøker instead of a more casual verb like sjekker
• hvorvidt instead of the more everyday om
• vocabulary like frostfri and temperert, which fit building/storage/property contexts

A more casual version might be:

• Vi sjekker om lagerboden er frostfri eller temperert.

That sounds more conversational, while the original sounds a bit more like something from a property description, inspection, or report.