"I have assigned variable names to each column of my matrix." This is not something that can be done in matlab. Matrices can only contain numbers, not strings. So, you've either converted your matrix into a cell array, split the matrix into individual variables (not a good idea at all!) or are using a table, which has explicit support for naming columns.
That last option (table) is the easiest way for you to achieve what you want. If you have not done so, convert the matrix to a table with array2table, then use writetable to save to disk. By default, writetable writes the column names as a header, so there's nothing special to do in your case.:
%yourmatrix: the matrix to write to text file
%columnnames: cell array of column names, e.g.:
yourmatrix = randi(100, 10, 4); %10x4 matrix for demo
columnnames = {'Pressure', 'Temperature', 'Volume', 'Heat Release'};
writetable(array2table(yourmatrix, 'VariableNames', columnnames), 'somefile.txt');
