Find months that == 6 with function find(). Then use index of this function to get the temperatures. Then use mean() on these temperatures.
Example:
% Creating random table to work with (similar to your table)
T = table();
T.Day = [1:1:17]';
T.Month = [1 2 3 4 4 5 6 6 6 6 7 8 9 10 11 11 12]';
T.Temperature = randi([29 32],17,1)
% Find position of all rows where Month == 6
idx = find(T.Month==6)
% Use idx to get all the temperatures
idxTemperature = T.Temperature(idx)
% Calculate mean
meanTemperature = mean(idxTemperature)
Edit: added an example
