A temple in Cuddapah where Sir Thomas Munroe is worshipped.

Sir Thomas Munroe — yes, the Governor remembered in the statue in the middle of Madras’s Island is worshipped in a temple in Cuddapah, Andhra Pradesh. There was a time in what were called the Ceded Districts when Munrolappa was not an uncommon local name.
This is an interesting article I read in 'The Hindu'

It was dark. Cuddapah was still quite far away. The gently sloping road ahead seemed to go on and on. “There is a temple on the way,” said one of our companions. “We must stop there. It is a small temple but a temple with an interesting story.”

The legend was that as Ram and Sita made their way back from Lanka to Ayodhya, Hanuman went ahead. He would search for a good place for the royal couple to stop and rest on their journey home. Not far from where we were was one such place. Hanuman had chosen a cave by the side of a river. To mark the spot, Hanuman hung a golden rope across two hill tops. So that from a distance the rope could be seen. The story continues. Ram and Sita did indeed stop at the cave. Grateful for Hanuman’s efforts, Ram etched a picture of Hanuman on the stone walls of the cave.

Centuries later :
Hundreds of years later, in British times, Sir Thomas Munroe was the Collector of Cuddapah. Travelling through the hills, late one night, he saw a gleaming rope of gold stretched from one hill top to another. “What is that” he asked his companions. “Why is there a golden rope hanging from one hill top to another?” There was a long silence. No one among Munro’s companions spoke. No one could see the rope that Munroe was referring to. No one had the courage to speak.

Finally, an elderly man spoke up. “He who can see the golden rope is blessed. But he will die in a few months.” Thomas Munroe looked at his companions in disbelief and put the story aside as superstition. But it must have stayed with him. It is said that he even wrote about this incident in his diary. In a few months time, Munroe was dead.

We stayed silent. We could not see any golden rope over the river. The dark hills passed us by. Our thoughts going back and forth: the mythical story of Hanuman and the unlikely fate of Munroe. In some time we came to the temple. A small glow of light in the darkening night. There were hardly any people in the temple. A few priests were conducting the evening aarti.

It was easy to walk right into the inner sanctum of the temple. There was a carving of Hanuman on the stone walls as described. Parts of the carving had been covered in silver. Till today, Hanuman’s service to Ram was being acknowledged, celebrated and worshipped.

Out in the main hall, a few people sat on the floor listening to the aarti. High above on the walls were framed pictures. Most were of gods and goddesses. In the centre,
prominently displayed was one of Ram and Sita. The glass framing the picture had
been smeared with holy ash, haldi and kumkum. There was a garland of fresh
flowers encircling the frame.

Right next to Ram and Sita was a framed picture of Sir Thomas Munroe. Like the gods and goddesses around him, he too was covered in haldi-kumkum and crowned with flowers.

Another article about Sir Thomas Munroe is even more interesting and this had happened before the above incident occured. This might give a believer's insight into why Sir Thomas would be the chosen one for such a divine experience.

When Sir Thomas Munroe was the Collector of Bellary in 1800, the Madras Government ordered him to procure the entire income from the Math and Manthralaya village. When the Revenue officials were unable to comply with this order, Sir Thomas Munroe visited the Math for investigation.

He removed his hat and shoes and entered the sacred precincts. Sri Raghavendraswamy emerged from the Brindavan and conversed with him for
sometime, about the resumption of endowment. The Saint was visible and audible only to Munroe who received Manthraksha.

The Collector went back and wrote an order in favour of the Math and the village. This notification was published in the Madras Government Gazette in Chapter XI and page 213, with the caption "Manchali Adoni Taluka''. This order is still preserved in Fort St. George and Manthralayam.

All the priests in the Math were much annoyed about the incident, because in spite of their long and sincere service, Sri Raghavendra Swamy had not given them darshan. That night, Swamyji appeared in the dream of the chief priest and told him that as Prahaladha, he and Munroe were class-mates in Kritha Yuga and he was destined to perform this noble deed of solving the Math's problem. Hence the unique privilege.

UPDATE - 1 : This is an excerpt from another article on the web.

Sir Thomas Munroe, Governor of Madras Presidency, who believed he was cured of acute stomach pain by the grace of Lord Venkateshwara, created an endowment by gifting the village of Kotavayulu in Chittoor District, for a daily offering of a gangalam (still known as the Monroe gangalam) of pongal.