Can I place a large amp on its side?

I am trying to set up my system in my living room. Can I put an amp, in this case a Theta dreadnaught on it's side?Or will that hurt its performance?

I would advise against that idea. You'll create heat dissipation problems.
Ask the manufacturer. They will have more info on this question than anybody here.
You might hear more power supply noise since logically you will change the position of the power transformer.

Otherwise the performance should not be hurt.
With proper ventilation (i.e., a fan setup), you should be able to put it on its side.

This amp can be configured by adding power modules that take its output from 200 watts to 1000 watts. I don't know how your unit is fitted out -- perhaps you have it running two 200 watt modules. Given that the circuit design appears to be biased significantly into Class A operation, these amps tend to run fairly warm. The holes in the top and bottom are intended to let rising hot air flowing out the top work to suck in cool air into the bottom, in a flue-like process.

If you put the amp on its side, you will defeat this effect such that air flow will be reduced and the amp will get hotter than its designers intended -- not good. If your installation configuration dictates placing the amp on its side, I suggest you rig up a fan to force air through the holes to provide adequate ventilation. Good luck.
If amp get hot laying normally... putting it on it's side will probably be a bad idea.
I had some (long ago, in a galaxy far away) early Carver amps that always were cool to the touch, and had those puppies upended and no problems in several years of use.
If the amp get hot, I would not even try it, even with a fan! A fan taht blows enough air is going to be too damn noisy to use, and one that is quiet is not going to blow wnough air to work.
If the amp is hot to the touch (you can keep your fingers touching the hottest part, but it is uncomfortable) then it it TOO HOT to turn on it's side.
If it is just warm to the touch, at it's hottest externale part, you could probably up-end it and be ok.
no way, don't do it. are you mad? it will likely cut the servace life in half.

put it on all four feet with at least 6 inches overhead clearance.