Yes, screen printing does require heat to cure the print. The curing process heats the ink to a certain temperature which bonds the pigment, and evaporates the water in the ink.  This ensures that the print is wash fast and permanent.
The best options to cure screen prints are:
Tunnel dryers.  This is by far the best option, although expensive, is worth the investment.  resulting in an even distribution of time and heat.
Flash Cures, this is a cheaper alternative, best for touch drying the ink before making another pass with another colour.
Heat guns – better for small prints, takes time and can be hit and miss.