What Exactly are These Connectors Called?

So I've been having issues with my TV being all screwy... it's an older DLP model, so there's all kinds of wonderful electromechanical stuff happening between the color wheel and the micromirror device. Well, it turns out my color wheel is going bad, so I took it out to have a look. It seems like the connector to the tach sensor sits perhaps a bit too close to the 120W mini-sun that gives the light (a.k.a. the lamp).

Anyways, the rear of the connector essentially crumbled, taking the inner pins with it. The insulation on the wires was nearly burnt off and the conductor was exposed on parts. Well simple, I just need to get a new connector, and possible rig up some sort of heat shield to prevent this from happening again.

The only problem is I have no idea what I am searching for! The "bad" end has a .1" pitch between the three pins, while the other end has four pins with only three connected. The whole connector is .5cm wide. I'm sure I can find a spare one of the bad connector laying around with my hoards of parts, but for my knowledge, what the heck are these things really called so I can find them on Digi-Key or Mouser or even eBay? I know it's a simple question, and I feel like a total n00b asking it!

Thanks for your help!

Wow, I forgot to add the picture:

Some kind of mini Molex?

Yeah that's probably the best I would have thought of.
.1" 3 pin mini molex

Mowcius

Or maybe "3-pin JST female".

I'd call it a JST