As you heat up, your Mech will move slower and slower, and torso twist will drop significantly. In addition, your HUD will get harder to read the hotter you are. If you get too hot, your Mech will shut down completely, leaving it vulnerable. If you're in the desert, obviously your heat will rise as a result. If you're hip-deep in water, your heat rating will fall.
Rain is also a heat-dropping factor.
Avoid explosions or Mech destruction. Being too near either of these things can cause instant Mech shut down. In addition, using beam weapons too much is a heat management no-no. You can't expect to fire a PPC, large laser and pulse laser at the same time repeatedly and not heat up. Group weapons wisely to avoid this.