Create GeoTIFF from JSON in python3

Question

For learning Python/GDAL I want to create a GeoTiff from the NOAA Aurora forecast data in Python3. I can already create an XYZ file:

import urllib.request, json 
import shutil
import os

tempfile="aurora.tmp"
outfile="/out/aurora.xyz"

with urllib.request.urlopen("https://services.swpc.noaa.gov/json/ovation_aurora_latest.json") as url:
    data = json.load(url)
    f = open(tempfile, "w")
    for coords in data['coordinates']:
        line = "%d %d %d\n" % (coords[0]-180, coords[1], coords[2])
        f.write(line)
    f.close()
    shutil.copyfile(tempfile, outfile)
    if os.path.exists(tempfile):
      os.remove(tempfile)

How would I go about writing an EPSG:4326 GeoTIFF (or any GDAL raster for that matter) from this data?