I haven't worked with time series data much. But, maybe instead of wide format you could try long format. Look at
gather and
spread functions in R. I'm envisioning you facet/color by the mesh (I don't know what mesh is). I don't really know what you're going after. But, it's usually a matter of structuring the data so that ggplot syntax will work. There is an as.numeric() function for converting to numeric values. I simulated some data to show what I mean.
i.e.
time temp mesh
1 4.12 0
2 5.34 0
1 6.56 1
2 4.78 1
1 6.12 2
View attachment 3116