Type of process of a system of high specific heat interacting with a system of low specific heat

Consider two systems A and B. Let the Molar Specific Heat Capacity of A be very, very, very, very great. The walls of (A+B) be of adiabatic nature from three sides and diathermal from another side (as in picture). A and B share a diathermal wall. Initially the temperature of A, B and Surroundings are the same. If we increase the temperature of surrounding then heat transfer will occur between surroundings and system B. Since A and B are separated by a diathermal wall then heat will also transfer from B to A thus increasing temperature of A. Let the heat exchanged by B be low in magnitude such that there will be an infinitesimal change in the temperature of A (because of the high Specific Heat Capacity of A).
Now my question is :


1. Is this an quasi-static process ?
2. Is this process reversible ?


[![enter image description here](https://i.stack.imgur.com/uQv0M.png)](https://i.stack.imgur.com/uQv0M.png)


