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Tc[κ_] := t /. Chop[
  FindRoot[
    1 == (4 κ^4 NSum[ 2/3 Hypergeometric1F1[3/2, 5/2, -((2 κ^2 l)/t)], {l, 1, Infinity}] 
           + 2 κ^2 t (PolyLog[1, Exp[(-2 κ^2)/t]]) 
           + 2 t^2 (PolyLog[2, Exp[(-2 κ^2)/t]] 
           + (2 κ^2)/t PolyLog[1, Exp[(-2 κ^2)/t]])),
  {t, tstart}, AccuracyGoal -> 8, PrecisionGoal -> 8]
 ]

tstart = 0.5; ni = 100; κmin = 0; κmax = 1; 
dκ := (κmax - κmin)/(ni - 1);
dat = Chop[ Table[{κ = κmax - (i - 1) dκ, Tc[κ]}, {i, ni}] ]; 
ListLinePlot[dat]

Mathematica cannot plot for ni=100 points. It just keeps on running for hours, but it does produce a plot for a very small number of points, e.g. ni=5.

How could I tackle this problem?

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