Finding the longest substring of string (case non-sensitive)

Question

I need to write a case non-sensitive code that finds the longest substring of any string and returns the corresponding part of the original string without affecting the original case.

A unique substring cannot contain any repeated letters.

It should work like this: ghHcd => Hcd

My attempt is below but it is stuck in an infinite loop due to reasons which are beyond my understanding.

Edit: My goal is to achieve this without using regular expressions.

def longest_unique_substring(text):
    longest_substring = ""
    temp_string = ""
    i = 0
    while len(text) > i:
        if text.lower()[i] not in temp_string.lower():
            temp_string += text[i]
        elif text.lower()[i] in temp_string.lower():
            if temp_string > longest_substring:
                longegst_substring = temp_string
            temp_string = ""
            i -= 1
            continue
        i += 1
    return longest_substring

Answer 1

This modification works for me:

def longest_unique_substring(test):
    longest_substring = ""
    temp_string = ""
    for char in test:
        if char.lower() in temp_string.lower():
            temp_string = temp_string[temp_string.lower().rfind(char.lower())+1:]
        temp_string += char
        if len(longest_substring) < len(temp_string):
            longest_substring = temp_string
    return longest_substring

Now longest_unique_substring('ghHcd') outputs 'Hcd'