I think David_sd has a great answer, I'll add how you might adapt his approach to be smoother, or else how you could potentially use plotly.

import numpy as np
from matplotlib import pyplot as plt
# Prepare data
n = 100
cmap = plt.get_cmap("bwr")
theta = np.linspace(-4 * np.pi, 4 * np.pi, n)
z = np.linspace(-2, 2, n)
r = z**2 + 1
x = r * np.sin(theta)
y = r * np.cos(theta)
T = (2 * np.random.rand(n) - 1)  # Values in [-1, 1]

If you don't need the colormap, you can get a 3d curve very easily. It's a shame that you can't pass a colormap argument into the plotting function as you can with the scatterplot/surface plot options you mentioned.

ax = plt.figure().add_subplot(projection='3d')
ax.plot(x, y, z)

To apply a colormap, I'd use the same approach as David_sd (with the limitations you identified).

# Build segments for Line3DCollection
points = np.array([x, y, z]).T.reshape(-1, 1, 3)
segments = np.concatenate([points[:-1], points[1:]], axis=1)

where points is a (100, 1, 3) representation of the points in space:

array([
[[ x1, y1, z1 ]],
[[ x2, y2, z2 ]],
[[ x3, y3, z3 ]],
...
])

and segments is a (99, 2, 3) representation of the point-to-point connections:

array([
[[ x1, y1, z1 ],
[ x2, y2, z2 ]],

[[ x2, y2, z2 ],
[ x3, y3, z3 ]],
...
])

then you run the following, using T[:-1] to match the shape of segments.

from mpl_toolkits.mplot3d.art3d import Line3DCollection
from matplotlib.colors import Normalize

norm = Normalize(vmin=T.min(), vmax=T.max())
colors = cmap(norm(T[:-1]))  # Use T[:-1] to match number of segments

lc = Line3DCollection(segments, colors=colors, linewidth=2)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.add_collection3d(lc)
plt.show()

This of course doesn't have the smooth gradient you want. One way to approximate that could be to pump up n -- e.g. here I set n=1000

If that's not satisfying, I might switch to plotly , which gets a pretty good gradient even with n=100

import plotly.graph_objects as go
# Create 3D line plot with color
fig = go.Figure(data=go.Scatter3d(
    x=x,
    y=y,
    z=z,
    mode='lines',
    line=dict(
        color=T,
        colorscale='RdBu',
        cmin=-1,
        cmax=1,
        width=6
    )
))
fig.show()