There are many connections between Iran and Hitler and I am the best person to answer this, since I recently wrote a paper on it. Persians and Germans, are both from the Aryan race. The Aryan invasion theory states that the Aryans started out from Persia and throughout years ended up in the Germanic tribes.
So truly, Persians are the true Aryan race. Hitler's master race theory was based on the fact the Aryan race was the purest and the lead. And since Persia was the home of Aryans, since the beginning of Hitler's political life, he had a positive attitude towards Persia. In 1935, when the world was watching as Hitler came to power, the Persian ambassador to Germany sent a cable to Reza Khan, the first shah of the Pahlavi dynasty, stating that Hitler will be a powerful man and in order to have great relations with him, Persia should change its name to Iran, which means "The land of the Aryans".
On March 21, 1935, cables were sent to all ambassadors around the world, to tell the countries to from now on refer to Persia as Iran. Later on during the Second World War, Iran did not want to join the Axis and to be seen as an evil, hence they stated that they were neutral, when in fact many German agents were working in Iran. Due to International Pressure, Iran finally joined the allied forces and declared war on Germany on 9 September, 1943. England and Russia saw Iran as the fastest route to transport supplies to troops in Russia, but Iran said "NO", since it was neutral.
So the British and the Russian forces invaded Iran, a neutral country and hence breaking international law. Between November 28 and December 1, 1943, Stalin, Roosevelt, and Churchill the leaders of the three major Allied forces held the Tehran Conference. This conference was a major event, since the main discussion was about the final attacks on the Nazis.
Additional info: Did you know hitler drove Reza Khan's Mercedes 500K from Iran to Russia to check up on his troops and that the car is currently on display at the National Car museum of Iran.