what kind of tropical turtle are you referring to? Just an aquatic turtle? Yes, a regular heater and aquarium are fine for an aquatic turtle, but many species grow very large so you'd have to have a good size tank! We are talking dinner plate size or bigger. They do require UVB lighting and heat lamps, a good filter, and a basking area in which they would be able to get completely out of the water.
All turtles should have a uvb bulb and a basking spot, the uvb helps them grow and harden the shell be activating vitamins. I think it's vitamin D. The only reason you wouldn't need one is if you could take your turtle out into the sun for atleast an hour or hour and a half each day. You can use a heater if you have a decent amount of water in your tank, but don't set the tempature very high. The key to a sucessfull turtle tank is research (Google).
tank temps and water levels depend on what species of turtle we are talking about and if it's an adult or hatchling or juvenile! For example a hatchling RES (red eared slider) water temp is best between 78 - 80, but an adult RES is best 72 - 76! Size and what species have different needs!