Submersible pumps come in two pieces; the pump and the motor. They can be purchased separately, or as a factory assembled unit. Goulds is a respected manufacturer of pumps. They don't make motors. Franklin is a motor manufacturer, specializing in submersible pump motors. Both of these manufacturers have been around for a long, long time.
Franklin motors haven't changed much over the years. The 2 wire ones usually have built-in thermal overloads, the 3 wire ones usually don't. Just because you have 3 wires coming out of the wellhead doesn't mean you have a 3 wire motor. Check for resistance between all of the wires. If one wire is open (infinite resistance), then your motor is 2 wire, and the installer just didn't have any 2 wire cable handy.
To properly size the thermal overloads, we'll need to know the full-load amps of the motor. Of course, we don't have that information, but if we had accurate resistance readings between each of the 3 wire combinations (BLA to RED, BLA to YEL, and RED to YEL), we very likely could determine the HP of the motor, and thus the amps. We'd also need to know the approximate length of the wire (distance from the control box to the well, and depth of the well), and the wire size (gauge). You could also hook it up, turn it on, and measure actual current.
The reality of pump thermal overloads is this; it's just about impossible to overload a centrifugal pump that's properly installed. With centrifugal pumps, the HP needed decreases with rising pressure. About the only way to overload a submersible pump is to have a deep-well pump installed in a shallow well. It is possible however, for the motor to fail to start. This can happen in a number of ways, a bad capacitor or a bad start relay are the most common. Mineral deposits on the shaft and impellers can also lock it up, but it's rare. In this case, the motor sits there and hums until one of 3 things happens.
1) The thermal overload trips (if there is one).
2) The circuit breaker in the electrical panel trips.
3) The motor burns up.
Obviously, #3 is the least desirable, but if it's fed power and doesn't start in about 20 seconds, that's what happens.
The control box you described seems to be a sort of universal replacement. The reason it doesn't have thermal overloads in it is because it is designed for a range of motors, not one specific motor. The old box was designed specifically for the motor it operated, thus the thermal was properly sized.
The risk is up to you, if the old pump never tripped the thermal overloads, the new one likely won't either. On the other hand, article 430 (motors) of the electrical code requires that every motor be protected against overloads and failure to start. A properly sized circuit breaker will protect against failure to start, but a properly sized thermal overload or a set of fuses is needed for overloads. I really don't know how a manufacturer can get away with building a control box without thermal overloads, unless the instructions say that the installer needs to provide separate overload protection.
Rob