Furthermore, I am very grateful for the way in which I have not been made to feel a nuisance during my teaching placement: thank you for your advice and encouragement.
Not really, a period + a new sentence OR a semi-colon would be preferable.
Furthermore, I am very grateful for the way in which I have not been made to feel a nuisance during my teaching placement. Thank you for your advice and encouragement. (this option is the best one)
Furthermore, I am very grateful for the way in which I have not been made to feel a nuisance during my teaching placement; thank you for your advice and encouragement. (this option may be grammatically correct, but the two sentences really have different emphases, and so why link them with a semi-colon?)