Dear Sir,
Yes, you need some cooling, this is specified by the user manual of every board, a proper cooling should be in place in order to not damage the hardware.
We don't have much guidelines as this is really integration specific, in our facilities we use computer fans blowing directly on the hardware and in our integration project we use conduction cooling.
Old FMC150 are not supported on VC707 but new one are, if you provide me with your FMC150 serial number I can verify whether or not your FMC150 would work fine on VC707.
The VC707 has two FMC sites but they are not fully populated. You can check with the VC707 user manual and schematics and FMC150/FMC110 pinout in their user manual in order to understand if this combo would work or not.
Best Regards,
Arnaud