Пускай головокружение лёгкое, при перегреве сразу выйдем в предбанник.

Here пускай does not mean a command like let. It has a concessive meaning: even if, granted that, or let it be that.

So Пускай головокружение лёгкое... means something like:

• Even if the dizziness is mild...
• Granted that the dizziness is only slight...

Russian пускай and пусть can both do this.

Russian usually omits to be in the present tense.

So:

• головокружение лёгкое = the dizziness is mild

There is no present-tense word for is here, but it is understood automatically.

Compare:

• головокружение лёгкое = the dizziness is mild
• головокружение было лёгким = the dizziness was mild
• головокружение будет лёгким = the dizziness will be mild

Because this is not just a noun phrase like mild dizziness. It is a whole statement: the dizziness is mild.

Compare:

• лёгкое головокружение = mild dizziness
• головокружение лёгкое = the dizziness is mild

So the adjective comes after the noun because it is functioning as the predicate, not just as a normal modifier inside one noun phrase.

Because it agrees with головокружение.

Головокружение is:

• singular
• neuter
• nominative here

So the adjective must match it:

• лёгкий = masculine
• лёгкая = feminine
• лёгкое = neuter
• лёгкие = plural

This is standard adjective agreement in Russian.

При перегреве means something like:

• in case of overheating
• when overheating happens
• if we get overheated

It sounds a bit more general and situational than a direct если перегреемся.

This kind of при + noun is common in warnings, instructions, and general statements.

It is the prepositional case.

The preposition при normally takes the prepositional:

• при перегреве
• при температуре
• при необходимости

So перегреве is the prepositional singular form of перегрев.

Выйдем is the 1st person plural future of the perfective verb выйти.

It means we will go out / step out as one complete action.

That fits the sentence well, because the idea is an immediate response:

• при перегреве сразу выйдем = if we overheat, we'll immediately step out

If Russian used an imperfective form, the meaning would shift more toward process or repeated action. The perfective here sounds natural for a single concrete action.

Because Russian often leaves out subject pronouns when the verb ending already makes the subject clear.

Выйдем already means we will go out, so мы is unnecessary.

Compare:

• сразу выйдем = we’ll go out right away
• мы сразу выйдем = we’ll go out right away, with extra emphasis on we

Omitting the pronoun is very normal in Russian.

Предбанник is a very culture-specific word. It is the room before the main hot room in a баня—something like an anteroom, dressing room, or cool-down room.

So выйдем в предбанник means going out of the overheated room and into that cooler adjoining room.

The word is built from:

• пред- = before, in front of
• баня = bathhouse / steam bath

Because Russian uses different cases after в depending on whether there is movement or location:

• в + accusative = motion into somewhere
• в + prepositional = being in somewhere

Here there is movement:

• выйдем в предбанник = we’ll go out into the anteroom

Compare:

• мы в предбаннике = we are in the anteroom
• мы идём в предбанник = we are going into the anteroom

They are very close, and in this sentence they are basically interchangeable.

So both of these work:

• Пускай головокружение лёгкое...
• Пусть головокружение лёгкое...

A rough difference:

• пусть is often felt to be a bit more neutral
• пускай can sound a little more colloquial or expressive

But the meaning here stays the same.

Because the sentence has two clauses:

1. Пускай головокружение лёгкое
2. при перегреве сразу выйдем в предбанник

The first clause sets up a concession: even if the dizziness is mild.
The second gives the main action: if we overheat, we'll immediately go out into the anteroom.

Russian separates those clauses with a comma, just as English often does in similar sentences.