This is Ganesha, son of Siva and Parvati. Thumbikai Alwar part is explained in the second part of this blog. Four armed holding elephant goad (Ankusha) and a noose in his upper hands. His trunk is reaching out to his lower left hand. He is wearing a crown and the Srichakra could be seen. Standing relaxed with legs slightly bent. One of the trunks, right one, is broken.
As usual, his belly is prominent. One of the very few deities with a belly. Other than Kubera, Krishna is sometimes shown with a prominent belly. Chennai museum has an example of standing Krishna with a large belly.
Made for worship at home, this Ganesha has lots of age to it. This may date prior to the seventeenth century. The similarity with another Ganesha on this site is to be noted.
The bronze is about 6cm in height.
Now to the Thumbikai Alwar part. Thumbikai refers to the trunk and Alwar refers to twelve Vaishnavite saints who dedicated their lives to spreading Vaishnavism. But when Ganesha is depicted in Vaishnavite temple he is referred to as Thumbikai Alwar. One such example is in Parthasarathy Temple, Chennai. Ganesha, as Thumbikai Alwar, is housed in a niche on the right side of the second Gopuram.
One observation. It is not unusual to see Vaishnavite deities in Saivite temples, especially carvings on the pillars and paintings on the walls. In addition, there are several examples of Vaishnavites deities worshipped in Saivite temples. So far I have not come across any other Saivite deity depicted in Vaishnavite temples. Ganesha is an exception, but then he is an Alwar.