Si elle ne refroidit pas un peu, elle se casse plus facilement.

Si means if here. It introduces a condition:

Si elle ne refroidit pas un peu... = If it/she doesn’t cool down a little...

In French, you do not need to add alors for then in the second part, although you can in some contexts. French often just uses:

Si + clause, result clause

So this sentence is a normal if ... then ... structure, even without an explicit then.

This is very common in French when you are stating a general truth, a repeated result, or something that normally happens.

So:

Si elle ne refroidit pas un peu, elle se casse plus facilement.

means something like:

If it doesn’t cool down a little, it breaks more easily.

French often uses:

si + present, present

for general cause-and-effect statements.

Also, after si meaning if, French does not use the future tense in the si clause. So you would not say si elle ne refroidira pas.

Yes, if you want to talk about a specific future consequence.

• Si elle ne refroidit pas un peu, elle se casse plus facilement.
  = general rule / habitual result

• Si elle ne refroidit pas un peu, elle se cassera plus facilement.
  = future result in a particular situation

So the version you have sounds more like a general statement about how the material/object behaves.

That is the standard French way to say not with a simple verb.

• elle refroidit = it cools down
• elle ne refroidit pas = it does not cool down

With a simple conjugated verb, ne goes before the verb and pas goes after it.

In informal spoken French, people often drop ne:

Si elle refroidit pas un peu...

But in standard written French, ne ... pas is expected.

Yes. In French, nouns have grammatical gender, so a thing can be referred to as il or elle depending on whether the noun is masculine or feminine.

So elle here does not have to mean she. It may simply mean it, referring back to a feminine noun such as la pâte, la matière, la pièce, etc.

English usually uses it for things, but French uses il/elle based on the noun’s gender.

Refroidit is from the verb refroidir, which means to cool or to cool down.

Here, elle refroidit means it cools down.

This is the 3rd person singular present form:

• je refroidis
• tu refroidis
• il/elle refroidit

So elle ne refroidit pas = it doesn’t cool down

This is one of the most useful things to notice in the sentence.

Casser by itself is often transitive: it usually means to break something.

• Il casse le verre. = He breaks the glass.

But when the thing itself undergoes the break, French very often uses the pronominal form se casser:

• Le verre se casse. = The glass breaks / gets broken.

So here:

elle se casse plus facilement

means:

it breaks more easily

It is not really reflexive in the English sense of breaks itself. It is just the normal French way to express that the subject undergoes the breaking.

Un peu means a little or a bit.

So:

elle ne refroidit pas un peu

means:

it doesn’t cool down a little / it doesn’t cool down a bit

With a simple verb, expressions like un peu usually come after the verb:

• Elle chauffe un peu.
• Elle refroidit un peu.

When the verb is negated, the structure becomes:

ne + verb + pas + un peu

So the placement here is normal.

Plus facilement means more easily.

• facilement = easily
• plus facilement = more easily

This is a comparative adverb.

The comparison is implicit. In context, it usually means:

• more easily than if it cooled down a bit, or
• more easily than normal / than before

So French does not always need to spell out the second half of the comparison if it is already understood from context.

Here, plus means more, and before a consonant sound, it is usually pronounced plu (roughly plew), without pronouncing the final s.

So:

plus facilement
is usually pronounced approximately like
plu fasilman

That is different from some other cases where the final s can be heard, especially before a vowel in liaison, or in more emphatic speech. But in this sentence, learners will normally hear plu facilement.