The reddest that I know is Dynamite...I don't like pink or lavender so am always searching for 'red'! Dynamite is also known as Lagerstroemia indica 'Whit II' so you can search under that name, too. The foliage is superb - gorgeous bronze leaves - another thing that recommends it. Haven't had it long enough to know what the bark is like. Monrovia lists the bark as 'attractive' but that could have a wide range.
There are a bunch of others, none of which I've seen in the trade here (despite cm's being very common in this area as street trees, etc) but you might have them there. Here's a page from University of Florida Extension with some background. Googling 'red crape myrtle' gets you a fair number of hits, as well.

Here is a link that might be useful: UF Extension Red-Flowered Crape Myrtles

The plant is 'Whit II', Dynamite is a marketing device. This goes on all the time now, with what the unwary are liable to think is the name of the plant actually being a trademark or registered trademark, the cultivar name being something deliberately hard to use.

'Whit II' is from Carl E. Whitcomb (Lacebark Inc.) in Oklahoma, and has been discussed on his web site. I tried a liner (from forestfarm) on Camano Island (Island County, WA), it didn't take off (let alone bloom) even though on a south wall. I have also seen larger stock of this introduction offered at a Seattle garden center. But probably it needs a hotter climate, those crape myrtles that do manage to bloom in my area are either in the hottest possible planting sites or are less demanding of heat than usual, or both.

Dynamite is one of the best performers here...so your thoughts about heat may be correct. lIllinois ought to get hot enough; they just have to deal with winter dieback. OP you should find out which of the reds is readily (reddily!) available near you and performs well in your zone. You could even knock on the door of the house whose yard you saw it in...

Here's a list of red crapes. Some may be redder than others, but all are pretty reddish. If you want to use the list to pick one for your landscape, be sure to confirm the provided info.

Cultivar (TM Name)/ Height / Form / Mildew Resistance
Arapaho / 20'+ / upright / high
Centennial Spirit / 8'-12' / upright / good
Cherokee / 8'-10' / globose / good
Cheyenne / 8'-12' / rounded / high
Christiana / 8'-10' / upright / fair
Coral Sport / 8'-10' / upright / fair
Gamad I (Cherry Dazzle) / 3'-5' / small dwarf / high
Mandi / 6'-12' / dwarf / fair
Moned (Chica Red) / 2'-5' / small dwarf / fair
Moners (Petite Embers) / 5' / upright dwarf / fair
Monimp (Petite Red Imp) / 4'-5' / upright dwarf / fair
Okmulgee / 3'-6' / dwarf upright / fair
Red Filli / 1.5'-2' / dwarf spreading / fair?
Rubra Compacta / 6'-8' / compact / ?
Tonto / 6'-12' / compact globose / high
Victor / 3'-5' / upright dwarf / good
Watermelon Red / 20'-25' / upright / fair
Weeping Alamo Fire / 2'-3' / weeping, miniature / fair
Wit II (Dynamite) / 20'-25' / upright / good
Whit IV (Red Rocket) / 20'+ / upright / high
Whit V (Tightwad Red) / 2'-4' / dwarf / high
Whit VII (Siren Red) / 10'-12' / upright / high
Whit IX (Double Feature) / 6'-8' / compact globose / high

I've got 300 Dynamite Crape Myrtles growing and should be ready in 1 gallon pots by end of July. The bigger trees on the side are Dynamites

CrapeMyrtleGuy.com

Here is a link that might be useful: Crape Myrtle Guy