It's a very bad idea to have the fans running all the time, as there not needed, so warm up times will be longer which does the engine no good, not to mention the fans take massive power, hence why they cycle only when needed!

It's overheating for a reason, by simply turning the fans on you won't cure the problem!

Have you tested the relay to make sure it's working?

OP bypassed the fan switch to make the fans work, so that won't be the problem!

Depending on how long you have had them running permanently for there is a chance you may have burnt the wiring out etc!

Martin