Possible Problem w/ Fleas in my Chilean Rose's Tank

My male Chilean Rose finally molted this past Sunday on Aug 15th & had a successful molt ( I was so psyched!) & now I've noticed a few tiny black things (I'm guessing they're fleas), cause our 2 cats have them & 1 of my cats loves jumping up over Venom's tank screen cover to lay down & I'm guessing that the fleas are dropping off his fur & into my T's tank! I know that Tarantulas can get mites, but they're very microscopic in size or even ants. Do u have any suggestions of what I can do to rid the fleas from my T's tank??! I just feel like taking him out of their & soaking the entire tank w/ bleach & very hot water, but it's probably too soon to even start handling/picking him up, esp. since he just molted a week ago & his bodie's still hardening up! : I did turn off the heating pad to see if possibly the fleas would die off that way cause they do thrive in warm temps too!

Fleas will not harm your tarantular, since in most cases they are very host speciefic. In your case, fleas from a cat will not suck on tarantula blood (has a very distinctive mixture and is not "warm blooded" and does not run through veins like in mamals.
Do not use bleach for your tank !!!! It will leave mikroscopic paerts of residue that will harm your T.
Unfortunally there is not much you can do except changing substrate and rinsing the tank thourougly with hot water, if you want to clean the tank more intensive you may use liquiod dish detergend like dawn and rinse it of very very very good.
about hardening, your T, as for adults the timeline to be on the save side is 7 days or 1 week, after that time period even the biggest T is completly hard.
If you want to try to handle your T you are good to go.