Утром я везу бабушку к врачу, потому что у неё высокая температура.

Утром is the instrumental case of утро (morning). In Russian, some time expressions use the instrumental to mean in the morning / during the morning.

So:

• утро = morning
• утром = in the morning

This is a set, very common adverbial use:

• утром = in the morning
• днём = in the daytime / in the afternoon
• вечером = in the evening
• ночью = at night

So here Утром means In the morning.

Везти / везу means to transport by vehicle or to take someone/something by some means of transport.

So я везу бабушку к врачу means something like:

• I’m taking Grandma to the doctor
• more literally, I’m transporting Grandma to the doctor

Compare:

• нести / несу = to carry on foot, in your hands, on your body
• везти / везу = to take by vehicle
• брать / беру = to take, pick up, grab

So if you are driving Grandma, taking her by taxi, bus, etc., везу is the right verb.

Because бабушку is the direct object of везу.

The person being taken is the thing directly affected by the verb, so Russian uses the accusative case.

• бабушка = grandmother (dictionary form, nominative)
• бабушку = grandmother (accusative)

For feminine nouns ending in -а / -я, the accusative singular often changes like this:

• мама → маму
• девушка → девушку
• бабушка → бабушку

So:

• Я вижу бабушку.
• Я люблю бабушку.
• Я везу бабушку.

All of these use the accusative.

The preposition к means to / toward when you are going to a person or in the direction of something. It requires the dative case.

So:

• врач = doctor
• к врачу = to the doctor

This is a very common pattern:

• к маме = to Mom
• к другу = to a friend
• к врачу = to the doctor
• к учителю = to the teacher

So in the sentence:

• я везу бабушку к врачу

the destination is expressed with к + dative.

Russian often expresses to have with the structure:

у + genitive + [thing]

Literally, it is something like at her there is...

So:

• у неё высокая температура = she has a high temperature
• more literally, at her [there is] a high temperature

Examples:

• У меня есть машина. = I have a car.
• У него время. = He has time.
• У неё высокая температура. = She has a high temperature.

Here:

• она = she
• её = her
• after у, you need the genitive, so неё is used

This structure is extremely important in Russian.

Because the preposition у requires a special pronoun form.

After у, personal pronouns take forms like:

• у меня = I have / at me
• у тебя = you have / at you
• у него = he has / at him
• у неё = she has / at her
• у нас = we have / at us

So неё is the form used after a preposition.

Also note the ё:

• неё is pronounced with yo, not plain e

That is why it is у неё.

Yes. Russian commonly says высокая температура for a high temperature / fever.

Here:

• температура is feminine
• so the adjective must also be feminine:
  • высокий (masculine)
  • высокая (feminine)
  • высокое (neuter)
  • высокие (plural)

Because температура is feminine singular, you get:

• высокая температура

This is the normal medical expression in Russian. In English we might also simply say she has a fever, but Russian often uses high temperature in this context.

Grammatically, везу is a present-tense form. But with verbs of motion, Russian often uses present forms to talk about a planned movement in the near future.

So depending on context, Я везу бабушку к врачу can mean:

• I am taking Grandma to the doctor (right now / as part of current action)
• I’m taking Grandma to the doctor [later today / this morning] (planned near future)

Because the sentence starts with Утром, many learners may interpret it as a scheduled or intended action in the morning.

This is very normal in Russian and similar to English I’m taking Grandma to the doctor tomorrow.

Because потому что introduces a subordinate clause: because...

Russian normally separates this kind of clause with a comma.

So the sentence has two parts:

1. Утром я везу бабушку к врачу
2. потому что у неё высокая температура

The comma marks the boundary between the main clause and the reason clause.

This is standard Russian punctuation.

Yes. Russian word order is more flexible than English, because case endings show grammatical roles.

The neutral version here is:

• Утром я везу бабушку к врачу, потому что у неё высокая температура.

But other orders are possible for emphasis, for example:

• Я утром везу бабушку к врачу...
• Бабушку я утром везу к врачу...
• К врачу я утром везу бабушку...

These all keep roughly the same basic meaning, but the emphasis changes.

For learners, the original order is a good, natural one:

• time first (утром),
• subject (я),
• verb (везу),
• object (бабушку),
• destination (к врачу).

This is a very common question because Russian verbs of motion are tricky.

• везу comes from везти and means I am taking/carrying something or someone by vehicle in one specific direction
• езжу comes from ездить and means I go / travel regularly, repeatedly, or in no single fixed direction

So:

• Я везу бабушку к врачу. = I am taking Grandma to the doctor.
  One concrete trip.

But:

• Я езжу к врачу каждую неделю. = I go to the doctor every week.
  Repeated action.

So везу is right here because it describes one specific trip with Grandma.

A few useful pronunciation points:

• утром — stress on the first syllable: Утром
• везу — stress on the last syllable: везУ
• бабушку — stress on the first syllable: бАбушку
• врачу — stress on the last syllable: врачУ
• неё — stress on ё: неЁ
• высокая — stress on со: высОкая
• температура — stress on ту: температУра

Important:

• ё is always pronounced yo
• so неё is not ne-eh, but ne-YO

A rough pronunciation guide for the whole sentence:

Utram ya vi-ZOO BA-boosh-koo k vra-CHOO, pata-MOO shto u ni-YO vy-SO-ka-ya tim-pi-ra-TOO-ra.

Not perfect English-style transliteration, but it helps show the stress.