Моё сердце тёплое.

Because сердце is a neuter noun in Russian. A very common pattern is:

• nouns ending in -о or -е are often neuter
• nouns ending in a consonant are often masculine
• nouns ending in -а / -я are often feminine

So сердце, which ends in -е, is neuter. Grammatical gender in Russian is a property of the noun itself, not something based on meaning.

Because the possessive pronoun has to agree with the noun it describes.

Here, the noun is сердце, and it is:

• neuter
• singular
• nominative

So the correct form is моё.

Compare:

• мой брат — my brother
• моя сестра — my sister
• моё сердце — my heart

A common mistake for English speakers is to think моё somehow reflects the speaker. It does not. It reflects the noun сердце.

For the same reason: the adjective must agree with сердце.

Since сердце is neuter singular nominative, the adjective also has to be neuter singular nominative:

• masculine: тёплый
• feminine: тёплая
• neuter: тёплое
• plural: тёплые

So:

• тёплый чай — warm tea
• тёплая вода — warm water
• тёплое сердце — warm heart

They are in the nominative case.

That is because сердце is the subject of the sentence, and моё and тёплое agree with it.

So the structure is basically:

• Моё сердце — subject
• тёплое — predicate adjective

In other words, the sentence means My heart is warm, with the subject in the nominative.

In Russian, the verb to be is usually omitted in the present tense.

So:

• Моё сердце тёплое. literally: My heart warm.
• natural English meaning: My heart is warm.

This is completely normal in Russian.

So English:

• My heart is warm

Russian:

• Моё сердце тёплое

No separate word for is is needed here.

The letter ё is pronounced like yo and it is always stressed.

So:

• моё sounds roughly like ma-YO
• тёплое sounds roughly like TYOP-la-ye

A useful rough pronunciation of the whole sentence is:

ma-YO SYER-tse TYOP-la-ye

A few important things:

• ё is never unstressed
• it often changes both the sound and the stress
• after many consonants, it also makes the consonant sound softer

Because Russian spelling often preserves letters that are not fully pronounced in difficult consonant clusters.

In сердце, the cluster -рдц- is hard to pronounce, so in normal speech the д is usually not clearly heard.

So it is written:

• сердце

but pronounced approximately:

• сЕрце / SYERT-se

This is normal and something learners just have to get used to. Russian spelling is not always perfectly phonetic.

Yes — in many Russian texts, people do omit the dots and write е instead of ё:

• мое сердце теплое

But the intended pronunciation is still:

• моё сердце тёплое

For learners, it is much better to keep ё whenever possible, because it helps with:

• pronunciation
• stress
• avoiding confusion with words that really have е

So while natives often omit the dots in casual writing or print, you should learn these words as моё and тёплое.

Yes. Russian word order is more flexible than English word order.

The basic version here, Моё сердце тёплое, is straightforward and easy to understand.

But other orders are possible, for example:

• Сердце моё тёплое
• Тёплое моё сердце

These alternatives can sound more:

• poetic
• emotional
• emphatic
• literary

So the sentence you have is a good neutral learning model, but it is not the only possible order.

Yes, Моё сердце тёплое is grammatical and understandable, but by itself it can sound a little poetic or emphatic, especially if it is meant metaphorically.

A very natural alternative is:

• У меня тёплое сердце

This is closer to I have a warm heart.

The difference is roughly:

• Моё сердце тёплое = My heart is warm
  Focuses directly on my heart
• У меня тёплое сердце = I have a warm heart
  Often feels more natural in everyday speech

So both are correct, but they are not identical in tone.