I don't know which country you are in, but uk, Maplin sell heated vests and heated footbeds that run on batteries. If you are touring and staying in hotels/b&bs, then you can take a pocket battery recharger..

A simple heated vest works extremely well at keeping you warm. You want to keep the core warm and your heart will pump warm blood out the extremities.
I just use a heated bib from Aerostitch in the USA, I like it because it's small and can pack it with me all the time.
But there's a good company in the UK who makes top of the line heated vest, google heated motorcycle gear.

I'm a male, living and riding in Australia on a fully faired bike, and supposedly I shouldn't get cold - but I do.

My solution, the complete head to toe Gerbings set up - jacket (not just a vest, arms get cold too), gloves, pants liner and socks powered by a dual heat controller.

I bought all these second hand off eBay US around 4 years ago at a very good price... and right now is the best time to purchase them as the US summer is now here, and many riders have forgotten the cold and are selling off their winter gear very cheaply.

Honestly, it is the best investment I have made in riding gear. I find heated gloves are so much better than grip heaters (which only heat the palms of your hands - totally useless when it is the tips of your fingers that are freezing).

As others have said, good modern cordura gear (forget leathers), technical layers like merino and micro fleece and an electric vest will do the trick. That way you can easily adapt- my wife swears by her Keis vest and modern gear allows you to zip in or zip out layers in your jacket and strides as required.

I feel the cold too :(
lots of great advice here - I'm a fan of merino wool but it is expensive (Aldi or Lidl do a great one for about £15!)
In the main, if you can eliminate the wind, you remove most of the chill factor.
There's some great technical materials on the market - EDZ do a jacket that feels a bit like a bin liner but it's meant to be 100% windproof. Also search cycle & "proper" outdoor shops. Heated vests are good but sweating can make you cold again :(

as Tiff said, pillions are fairly stationary, so stop lots for hot drinks, warm food & a bit of a walk :)

I think most have covered it here.
I would also suggest merino baselayers: spend the money on the good stuff it is not so scratchy.. icebreaker has different grades so you can chose temperature level (i assume others do to), wool aslo works when wet many synthetics dont.

an other advantage of merino is that it is naturally bacteria resistant.. so it dont smell for a lot longer then any of the synthetics.. :thumbup1:

Lots of layers are better then one (easy to mix and match) cus if you get too hot ; even a little sweat will decrease the effectiveness of many types of thermal layers.

ALSO cover the neck with a insulated/wind stopper "Buff" or other.. I made MRSX and I both leather ones with merino liners for our necks (wind proof with low thermal transport capacity). Many of your thermoreceptors are located in the carotid arteries of the neck. Even if our core is not "cold" the brain may think it is so you feel cold (or of course we could be cold there too, so dont only cover the neck). So spend some time/money on this too. :freezing:

Of course keeping our core warm is very important (like life and death important). But our extremities (especially hands and feet) are very well perfused (lots of blood) and have very very high surface to mass ratios.. this by definition causes heat loss. which then cools the core which then shuts down the blood to the extremities.. which makes them colder.. which mean the blood there is even colder...hypothermic cycle... So cover em up well as well.

I have both a Keiss vest ( brilliant) and ''Seal skin'' waterproof socks ( both warm and dry). One thing that is very important though , and I don't think mentioned so far is to make sure the kidneys are kept warm, especially for the pillion. Get a good kidney belt, wear it over the first layer shirt or whatever and underneath the heated vest. Keeping the draft out of the head and neck is also important. A silk balaclava and neck buff are essential pieces of kit IMHO