The watt rating is absolutely critical to the operation of the device.
The high heat is a direct result of too much amperage flowing through the dimmer.
Reduce your wattage immediately or stop using the dimmer.
You have a fire hazard.
According to the math, you have 20 - 65 Watt bulbs
Change 12 of the bulbs to 40 watt and you will drop to the 1000W max.
12 x 40 = 480W
8 x 65 = 520W
Total = 1000
However I am worried about this circuit.
A typical 15 amp switch (not a dimmer, but the switch) is maxxed-out at 1440 Watts.
So if you had 20 100 watt bulbs for 2000 Watts, it would heat up the 15 amp switch
It seems very odd that an electrician would put 20 lights on one circuit without having a 20 amp switch and 12 gauge wire.
Look at the markings on the switch you replaced and look for amps or watts.
And then look at the color of the wire cable inside your box ... 12 gauge wire is yellow and the lighter-weight 14 gauge wire is white.
If you have a white wire going to all those lights, then you are going to burn down the house unless the total wattage is reduced.
Volts X Amps = Watts.
I think your circuit needs a review to make sure it has the correct wire.http://waterheatertimer.org/Color-codewire2.html
This being said, Lutron
makes 1800 Watt dimmers.
You can web search: 1800Watt single pole dimmer
If you have yellow-colored 12 gauge wire, it can carry up to 1920 Watts
If you want more help, add a comment and I will answer