You can use circshift to rotate your data in a circular fashion. Once you have the circular shifted data, you can just manipulate the coastlon to get the longitudenal range starting from 0 to 360.
Here is an example using reanalysis data.
clc
clear
file='gdas.txt'; % this is really a netcdf data,
% %but I have changed just the file extension to attach this file here in the answers
lon=ncread(file,'lon');
lat=ncread(file,'lat');
tmp=ncread(file,'tmp');
load coastlines
figure
contourf(lon, lat, tmp', 'linecolor','none')
hold on
plot(coastlon, coastlat, 'k-','LineWidth',0.2)
caxis([200 320])
colormap(jet(12))
daspect(ones(1,3))
xlim([-180 180])
colorbar
coastlon=mod(coastlon,360);
coastlon(abs(diff(coastlon))>100)=nan; % commenting this line results into mutiple
% horizontal lines in the plot
figure
contourf(lon, lat, circshift(tmp,size(lon,1)/2,1)', 'linecolor','none')
hold on
plot(coastlon-180, coastlat, 'k-','LineWidth',0.2)
index=sum(lon==get(gca, 'XTick'),2);
xticklabels(lon(logical(index))+180)
caxis([200 320])
colormap(jet(12))
daspect(ones(1,3))
colorbar
