Hi Auato: No you are not limited to Firmware (FW) than version .07, or a newer FW won't necessarily fix your problem. But you can go up to the very latest FW in your DSA815/or DSA815-TG, which I believe is .19.03. Although you should install .11, and possibly .12 first before going higher than FW .12. Please ask PeDre about this, as he is a expert on the DSA815 including its FW.
Please note that I'm NOT saying that installing later FW will fix your issue, but I thought that you should understand and appreciate that you don't have a Firmware limitation on your particular DSA815. PeDre can correct me if I'm wrong, but I feel do feel confident in what I've said. PeDre may even have the essentially the same DSA815 hardware configuration (?) that you have there, or he will at least be very familiar with it.
Why do you feel that the issue you have in your unit is with the Spartan FPGA? Of course it could be, but I'm curious as to why you primarily to suspect it?
Using a Heat Source is usually to find a component that is currently working, but fails after being turned for a while (that has heated up for a time), not for a problem right off from just being turned ON. Or using Cold Spray for helping to find what failed after it had been ON and working, and then failed after being ON for a length of time.
Its not too likely that you are just going to see something that caused the problem. Of course it does sometime happen that you will find a obvious burned, cracked, or hot item. This is possible and we have all seen this, although its rare and usually associated with a catastrophic failure due to a shorted component, etc. It can happen, although rarely. Unless when you say see something, did you mean with an oscilloscope?
Good luck, and if you have more information we/someone may be able to provide ideas for you to look into. And telling us your technical capability would also help determine the type of suggestions to offer you to consider looking into.
Cheers, Ted