Rum does not go bad in the heat.
However when rum is left out in the heat the rums alcohol content becomes diluted and the rums taste will change and not be as good.
The rum itself will still be safe to drink even when left out in the heat but it won't be as enjoyable.
So it's best to keep the rum out of the heat and store the rum in a cool place.
Heat does not make alcohol stronger.
Instead heat makes alcohol weaker because the heat causes the alcohol content to become diluted so the alcohol content will be less and the alcohol will not taste as good.
Heat is never good for alcohol.
When alcohol gets hot the alcohols alcohol content gets diluted and the alcohol tastes different and not as good.
The alcohol is safe to consume when left in a hot car after you cool it down but it's not gonna taste very good after the alcohol has been left out in the hot car longer than a few hours.
Alcohol is OK in a hot car for a short time.
However if you leave alcohol in the hot car too long it can dilute the alcohol content in the alcohol and then the alcohol may not be as good.
Leaving alcohol in a hot car for a few hours should do no harm to the alcohol but you should never leave the alcohol in the hot car longer than a few hours.
I've left alcohol in my hot car before for a few days and the alcohol changed in taste even though I refrigerated the alcohol to cool it down.
The alcohol never tasted the same but was still okay to drink.
So if possible remove the alcohol and store it in a cool place until you're ready to consume it.