I have this code:

phi[t_] := t_0 + c*Exp[-k*t];
k = 1.5; t_0 = 60;
Thread[
  Plot[Table[phi[t] /. c -> i, {i, -15, 15, 5}], {t, 0, 3}, 
    PlotRange -> {45, 75}]]

Which, as expected, produces the plot:

However, mathematica is also spitting some weird error messages at me:

Thread::tdlen: Objects of unequal length in cannot be combined.

When I hover over the image in the error I get a list of a dozen other error messages:

RGBColor called with 1 argument; 3 or 4 arguments expected.

Coordinate Skeleton[77] should be a pair of numbers, or a Scaled or Offset form.

Coordinate Skeleton[77] should be a pair of numbers, or a Scaled or Offset form.

Coordinate Skeleton[77] should be a pair of numbers, or a Scaled or Offset form.

Coordinate Skeleton[52] should be a pair of numbers, or a Scaled or Offset form.

Coordinate Skeleton[77] should be a pair of numbers, or a Scaled or Offset form.

Coordinate Skeleton[77] should be a pair of numbers, or a Scaled or Offset form.

Coordinate Skeleton[77] should be a pair of numbers, or a Scaled or Offset form.

I searched for the three different types of error messages given and none of the results I found seem to be relevant to my “problem” (If you can call it that: my graph looks fine, mathematica is just complaining for some weird reason).

Is this a bug, or is there something subtle that I’m doing wrong?

Plot has the native ability to “thread” the functions.

phi[t_] := t0 + c*Exp[-k*t];
{k, t0} = {1.5, 60};
Plot[Table[phi[t] /. c -> i, {i, -15, 15, 5}] // Evaluate, {t, 0, 3},  PlotRange -> {45, 75}]

Also note that t_0 is not $ t_0$ as in $ \LaTeX$ , because t_ represents the Blank[] pattern associated with t.

And you can force the evaluation of the argument to Plot with Evaluate to make different colors.