For an example, take a look at this guy who glued 5000 flat mirrors onto a satellite dish to "start a fire", and some more :) Ironically, it was destroyed in an unrelated fire accident later...
Solar Death ray with 5000 flat 1x1 cm mirrors
The R5800 is my latest and greatest solar creation. Made from an ordinary fiberglass satellite dish, it is covered in about 5800 3/8" (~1cm) mirror tiles. When properly aligned, it can generate a spot the size of a dime with an intensity of 5000 times normal daylight. This intensity of light is more than enough to melt steel, vaporize aluminum, boil concrete, turn dirt into lava, and obliterate any organic material in an instant. It stands at 5'9" and is 42" across.
Unfortunately, the R5800 was completely destroyed in a storage shed fire on December 14, 2010.
This question reminds me of Zeno's paradoxes.
It is assumed that the two mirror surfaces are absolutely parallel.
In classical physics the electromagnetic waves that create the reflections are uniform and the energy loss due to the reflection ( depending on the material of the glass) will be what will make the reflections fainter and fainter, but the process is continuous and the limit will be a limit in luminosity. In principle a totally reflecting material would have no limit, going to infinite reflections as time goes to infinity. {corrected from the original statement that the wavefronts are instantaneous: Maxwell's equations obey special relativity i.e. the velocity c of light is finite}
Reality is quantum mechanical and also special relativity dependent.
With special relativity in the problem it will take time to reach the next reflection, so even for a total reflector infinity will also be reached only at infinite time, during observation, though there will be an enormous number of reflections.
Quantum mechanically there can not be a totally reflecting mirror, even in a thought problem. There will always be a probability of absorption and thus termination of the wavefront eventually, the images getting less and less defined until they become individual photons and finally totally absorbed.
Since quantum mechanics reigns, in reality, no, there will not be an infinite amount of reflections.
Best Answer
This is a variation on a theme which has been discussed many times. For example, see Strength of moonlight
The short answer is no; you cannot heat an object hotter than the temperature of the source. The advantage of multiple passes with mirrors is that you may be able to extract more energy on each pass of the light - this is often done inside the cavity of a laser, in order to extract the maximum energy from the pump beam.
But for sunlight you might do better by simply improving the absorption rate of your final collector.