Nope it does not. It has a black finned heatsink at the top held on by two thumb screws.

Check that the correct lamp is in. Though the contact connector would usually only allow the correct lamp, I have seem some beat up connectors that look almost forced apart at the sockets. A bulb/lamp with the wrong wattage would probably make much more heat.

If I remember it should be a Esj bulb, not 100% so double check it to the manual.

I would not worry with a bit of heat, keep the work area clear and you should be fine. I have never encountered popped negatives from a diffusion enlarger because of a hot lamp.