Iterative procedures are many times very sensitive to starting values. Sometimes one has to be very close to the correct estimates and sometime one just needs to start with the right sign. My guess that NonlinearModelFit uses 1 as the starting value for all parameters. If one uses -1 for the starting value for d, a good fit results.

Z = NonlinearModelFit[data, Ic, {x, { d, -1}, j}, T];
Z["BestFitParameters"]
Z["BestFit"]
Show[Plot[Z[T], {T, 4, 300}, PlotRange -> All], ListPlot[data] ]

Hi Marco, What you are saying, makes sense. This data should ideally head to infinite at T = 0, though experimental data points (specially close to T = 0) might be low in accuracy and hence the discrepancy. Anyways thanks for your help and figuring out the real problem as I was bit confused with what I was getting. Will write if have any further query.