October through April is prime time. Houston is flat and humid, and the cooler months are when most runners schedule goal races and long runs. Summer is for easy base miles.
Run at the coolest time of day. The National Weather Service advises moving strenuous activity to the coolest part of the day. In Houston summer that means sunrise. Watch the heat index, not just the temperature.
Drink before you're thirsty, and slow down. On hot, humid days run by effort instead of the watch, shorten the run or split it up, and carry fluids or plan a route past water fountains. The Seymour Lieberman Trail lists water fountains along its loop.
Dress for sun. Wear lightweight, loose, light-colored clothing, a hat or visor and sunscreen. A local Houston running store can help with apparel and hydration gear.
Know the warning signs. Heavy sweating, weakness and cool, clammy skin point to heat exhaustion: stop, get somewhere cool and sip water. Call 911 for confusion or slurred speech, which can be signs of heat stroke.
More on training through it: zone 2 and slow running in Texas heat.