Αν το θερμόμετρο δείξει πάλι πυρετό, θα πάω στη γιατρό αύριο το πρωί.

δείξει comes from the verb δείχνω (to show), but it uses the verb’s perfective / aorist stem: δειξ-.

So the main forms are roughly:

• δείχνω = I show / I am showing
• έδειξα = I showed
• να δείξει / αν δείξει = to show / if it shows

This stem change is very common in Greek verbs, so learners often need to memorize more than one stem.

Because this sentence talks about one possible future event.

After αν in this kind of future condition, Greek usually uses the perfective non-past form, which here is δείξει. It points to a single complete event:

• Αν το θερμόμετρο δείξει... = If the thermometer shows...

If you used δείχνει, it would sound more like an ongoing or repeated situation:

• αν δείχνει = if it is showing / if it keeps showing

So δείξει is the natural choice here.

Because in normal Greek conditional sentences, θα goes in the main clause, not in the αν-clause.

So Greek says:

• Αν ... δείξει, θα πάω ...

not:

• Αν θα δείξει ...

This works a lot like English:

• If it shows..., I will go...
• not If it will show..., I will go...

So the future meaning is expressed by the whole structure, and θα appears in the result clause: θα πάω.

Here πυρετό is a direct object in the accusative singular, and Greek often uses health-related nouns like this without an article.

Compare:

• έχω πυρετό = I have a fever
• έχω βήχα = I have a cough
• δείχνει πυρετό = it shows fever

Using τον πυρετό would usually sound more specific or marked, as if you were talking about a particular fever already identified in the conversation. In this sentence, the bare noun is the normal choice.

Because θα πάω refers to one complete future action: one trip, one visit.

Greek often uses:

• πηγαίνω for the imperfective idea
• πάω for the perfective / one-time movement idea

So:

• θα πάω στη γιατρό = I’ll go to the doctor
• θα πηγαίνω στη γιατρό would usually mean I’ll be going / I’ll go regularly

In this sentence, the speaker means a single visit tomorrow morning, so θα πάω is right.

Because some Greek nouns can be masculine or feminine even if the form stays the same. Γιατρός is one of them.

• ο γιατρός = the male doctor
• η γιατρός = the female doctor

In this sentence, the article shows that the doctor is female:

• στη γιατρό = to the female doctor

So in Greek, the article often tells you the gender more clearly than the noun ending does.

στη is the contracted form of σε + τη.
You may also see στην, from σε + την.

The final -ν in την is sometimes dropped before certain consonants, and before γ that is very common in everyday Greek. So:

• στη γιατρό = completely normal
• στην γιατρό = also possible, depending on speaker and style

So this is mostly a matter of pronunciation/spelling preference, not a change in meaning.

Because Greek normally uses the definite article with parts of the day:

• το πρωί = in the morning
• το βράδυ = in the evening
• το απόγευμα = in the afternoon

So αύριο το πρωί is the standard way to say tomorrow morning.

You may hear shorter forms in casual speech, but αύριο το πρωί is the normal full expression.

Because πάλι usually goes near the word or phrase it modifies. Here it modifies the idea of showing fever again, so:

• δείξει πάλι πυρετό

is a natural order.

It can move, but the nuance changes slightly. For example:

• Αν πάλι το θερμόμετρο δείξει πυρετό...

puts more emphasis on again as a discourse idea, almost like if, once again, the thermometer shows fever...

So the original placement is the most straightforward.

Yes. Greek word order is fairly flexible.

The original sentence begins with the condition:

• Αν το θερμόμετρο δείξει πάλι πυρετό, θα πάω στη γιατρό αύριο το πρωί.

You could also say:

• Θα πάω στη γιατρό αύριο το πρωί, αν το θερμόμετρο δείξει πάλι πυρετό.

Both are grammatical. The difference is mostly one of focus:

• putting the αν-clause first highlights the condition
• putting it later highlights the main action first

The comma in the original is normal because the conditional clause comes first.