Your function diverges as Y goes to zero. ContourPlot apparently cuts off the high values. Compare with Plot3D:

Plot3D[c1*x*L + 
  300 + (-0.05268836893878311` + 
     0.05268836893878311` E^(-18.979521127315678` Y) + 
     1.1437436762540135`*^-8 Y)*c2, {x, 0, 01}, {Y, 0, 1}]

You can control the cutoff style with ClippingStyle. For example

ContourPlot[
 c1*x*L + 300 + (-0.05268836893878311` + 
     0.05268836893878311` E^(-18.979521127315678` Y) + 
     1.1437436762540135`*^-8 Y)*c2, {x, 0, 01}, {Y, 0, 1}, 
 ContourStyle -> None, ClippingStyle -> Automatic, 
 ColorFunction -> "Rainbow", Contours -> 60]