There is no te-form for saying thank you because "thank you" is not a verb nor an adjective.
If you want to continuously thank someone, like repeating "thank you, thank you", you can use another word the Japanese people often use (even more than Arigato) which is "*Domo*".
"*Domo domo*" (repeated two times) sounds more natural - and of course, shorter, than saying, "*arigato gozaimasu arigato gozaimasu*" :wink:
:idea: Now, back to the difference of *arigato gozaimasu* and *arigato gozaimashita*...this is a bit tricky, because in a way, there is no clear line between the usages of each one.
A person gives you a gift, _grammatically_*arigato gozaimasu* makes more sense, since you are receiving it NOW, in the present. :cry:
A person gave you a gift yesterday, and you want to thank her/him for this TODAY, obviously, in this case, it's appropriate to say *arigato gozaimashita* - thanking her/him for the giving which happened yesterday.
Having said that, you may hear a Japanese person saying *arigato gozaimasu* referring to something in the past.... sorry! there seems to be no clear cut rules :shock: