I like the heatpress vinyl for phrase inspired designs and simple graphics. This stuff is great for custom quick orders and its durable. One offs which most printers turn away can now be done easily and for a profit. Comes in a variety of colors and textures, easy to store and no messy chemicals to deal with.
Any large plastisol ink, transfer, or heatpressed vinyl design can be hot in direct sunlight. I am wearing a screenprinted show shirt right now and it gets hot around the design. Text designs in vinyl regular sized isnt going to be so bad...its the oversized stuff that gets ya. Most sports teams use some sort of vinyl transfer for names and numerals. You can cut them yourself with a plotter or order them ready made with names and numerals for your team.