Unusual heat rise on rectifier
Its going to come downto powerflow and how "DC" your DClink is.

Without the cap the 55W bulb will be provided with ABS(Sin) voltage 



This provides an RMS voltage of Vpk/1.414 and thus the power reduced.
the 55W/12V bulb is an equiv of: 2.618R
with an XFMR giving out 14.1pk voltage => 9.97Vrms => 37.98W

Now when you add the capacitors, you are "smoothing" the DClink

This increases the power supplied to the resistive load as it is now a DClevel.
20mF worth or capacitance should provide a DC output.
14.1V on the DClink =>  75.939W
Increased power, increased heating.