The pulsing is normal, that's due to the watervalve opening and closing, so now you also know the valve is working OK. This has the newer style valve, it's pretty dependable, no rubber bellows to rip like the old style valve.
Possibly you are low on coolant?
Other than that, the first few things to think of would be :
1.intermittent loss of voltage, maybe a crack in a fuse causing this?
2.interior temp sensor bad
Unsure what the noise has to do with it, unless the low on coolant is true, and maybe it gurgles due to air in the coolant stream?
Does the noise correspond with when you have problems? Just what is the exact complaint, that the temp fluctuates or what? Or is it a fan problem, or is the air coming out where you don't expect it to? What does the noise sound like?