I don't know...consider the Professor...I asked one of the most popular Professors in my dept. to write me a rec. letter. It was for business school and he was an English professor. It turned out he accidentally mailed the letter to me instead of the Uni I'd appled to. In the meantime I'd gotten my CFO to write me one that I thought would have more 'weight' in business school than an English Professor, so I opened the letter from my English Professor.
It said, "I have never worked with a better student than Westclock." I was like...dude..my name's Sen Say. So, obviously he had a form letter where he just filled in people's names. Or, maybe he only used the form letter for people that sucked and he couldn't think of anything to write, but I think the fact that so many people asked him for references (I mean basically 100% of English UnderGrads need to go to Grad School) led him to just copy and paste names.
So, if you ask the most popular Professor, no need to send a thank you as he probably fucked you over by not putting the right name on the letter.
On the other hand, if you have a Professor that no one likes and you ask him to write you a letter of recommendation then maybe you could send him a thank you card. But, if no one likes him and you're asking him to write a letter he's probably a homo or a ped and either way will expect you to properly thank him by letting him suck your cock or paint your nails or clean his stainless steel kitchen appliances for him with steel wool on a lazy Sunday afternooon, so when he gets your thank you card he'll tear it up and hope you don't get into grad school.