Thompson, who celebrated his 48th birthday on Friday, took charge of the Tangerines' loss at Derby County yesterday after Ian Holloway was announced as the new Crystal Palace boss earlier in the morning.
Holloway took Keith Millen with him to Selhurst Park but Thompson is happy to stay at the seaside club.
"It is all up to the chairman but I will get another chance to show my credentials when we play Sheffield Wednesday on Tuesday," he said.
"I'd like to think that the things the club has achieved in this period will be remembered because I believe I have played an important part."
"I've been a number two here and I've had some good times here. I've had two promotions, three Wembley visits and I'd like to think I've been a part of that."