1. Query Accounts put it in a map<Id, Rating> 2. Query and get related records, map of account to related records 3. If Rating is Hot then update all the child records with Hot so on and so forth

AccountContacts.java

public class exploreTestOne {
    
    String localAccountId;
    Set<Id> accountIds = new Set<Id>();
    
    List<Contact> finalContacts = new List<Contact>();
    
    public Map<Id, List<Id>> accountContacts{set; get;}
    Map<Id, String> accountRatingMap = new Map<Id, String>();
    public exploreTestOne(){
        accountContacts = new Map<Id, List<Id>>();
    }
    
    public void foobar(){
        
        List<Account> accounts = [SELECT Id, Rating FROM Account];
        
        Map<Id, Account> accountsMap = new Map<Id, Account>([SELECT Id, Rating FROM Account]);
        Map<Id, Contact> contactsMap = new Map<Id, Contact>([SELECT Id FROM Contact]);
        
        for(Account a : accounts){
            accountRatingMap.put(a.Id, a.Rating);
        }
        
        AggregateResult[] groupedResults = [SELECT Id, AccountId FROM Contact WHERE AccountId IN: accounts GROUP BY Id, AccountId];
        
        for(AggregateResult ar : groupedResults){
            localAccountId = (Id)ar.get('AccountId');
            
            if(accountIds.contains(localAccountId)){
                
                //get values and update the list in the map
                List<Id> existingList = accountContacts.get(localAccountId);
                existingList.add((Id)ar.get('Id'));
                accountContacts.put(localAccountId, existingList);
            }else{
                //add a new entry into the list and add it to the map
                accountIds.add(localAccountId);
                List<Id> onlyId = new List<Id>(); 
                onlyId.add((Id)ar.get('Id'));
                accountContacts.put(localAccountId, onlyId);
            }
            
        }
        
        for(Id accountId : accountContacts.keySet()){
            List<Id> relatedContacts = accountContacts.get(accountId);
            
            Account localAccountRec = accountsMap.get(accountId);
            
            if(localAccountRec.Rating == 'Hot'){
                for(Id conId : relatedContacts){
                    Contact localContactRec = contactsMap.get(conId);
                    localContactRec.LastName = 'Hot';
                    finalContacts.add(localContactRec);
                }
            }
            
            update finalContacts;
        }
    }
    
    
}

AccountContacts.vfp

<apex:page controller="exploreTestOne" action="{! foobar }">
    {! accountContacts }
</apex:page>