You might get transient symptom relief, but will lose in the long run. Continued exposure to very hot water will only injure the already inflammed and sensitive tissue that is trying to heal. The same goes for scrubbing the area in the shower with a washcloth - feels good for a while, but you'll pay.
You would be better off being very gentle with the skin and use a topical steroid cream. The over the counter steroids (low concentration hydrocortisone 1% and triamcinolone 0.5%) will be OK for mild attacks, but more severe cases will need a higher class steroid like prescription clobetasol 0.05%. I favor the clobetasol over the other fluorinated steroids because it comes in a generic form (less $$$). The topical meds have an advantage as they give little systemic side effects. Really bad reactions will respond to a brief treatment (~ 7-10 days) of an oral steroid such as Prednisone. The often prescibed Medrol dosepak (a tapering dose over six days) does not give a high enough steroid dose over a long enough period to provide significant relief, and poison ivy will often "come back" with the dosepak.
Once your skin has been cleaned with soap and water, it will not spread by touching the affected areas or the weeping fluid from the rash. Rashes will come up on other areas at different times, based on the exposure amount and thickness of the skin. The oil can remain on work gloves, clothes, boots, and pet hair, and then be spread to other areas by repeated contact.
Try to avoid topical anti-itch medicines (such as those that contain benzocaine) as they can be very sensitizing to open skin (i.e., can cause allergic reactions and increased itching). It is interesting that oral Benadryl (diphenhydramine) works to prevent itching and allergic reactions, but as a topical agent it can be sensitizing. I'd avoid this medicine topically. Calamine can help dry out the lesions and decrease itching.
There are some other agents such as Zanfel that are highly advertised and highly priced. IMHO I'm not sure there is any advantage of these products, since most poison ivy gets well on its own
Free advice from a professional stunt doctor on a closed course - your mileage may vary.