Type of hood? Venting direction? Type of cooktop? Width? Depth? Desired CMF?

I have a 48" range set against the wall, and the hood will be 48" wide and 18" tall stainless steel.

This is a more complex subject than you might imagine, due to a combination of factors including such as your own preferred point in the cost, aesthetics, performance trade space, the fact that the hood is dealing with cooking plumes of various types, and that the hood performance (and safety) also depends on make-up air issues. Please review the references I provided in this recent discussion in the Kitchen Forum: https://www.houzz.com/discussions/6459657/what-vent-hood-for-an-induction-range#29189862. The links should be useful to familiarize yourself with the subject so we can refine your requirements.

Note that I deal with performance requirements; cost and aesthetics requirements are left to the OP or others who may chime in.

Thank you very much, Kaseki, for your helpful input. However, my original question was about the hood lighting. Whether or not the Thermador hood provides sufficient lighting. Since I have a Thermador range, I am looking for the Thermador hood to go with it. However, the Thermador lights under the hood do not seem as bright as many other brands. The hood is 25" deep; I imagine it will shadow the cooking area. Does anyone have experience with a Thermador hood, and how do they feel about it? Has lighting ever been a problem?

Sorry. I thought "this" applied to both sentences.

In any case, if the lights use a standard socket, there may be replacement LED lights that will fit and increase the illuminance.

The Thermador PH48GS has four G9-based 40-watt halogen bulbs. These bulbs are available up to 750 lumens each. Fortunately, the hood includes a dimmer as when these are on full blast the range surface will be way overlit. At ajmadison (you also need a blower).

If the halogen's are too hot over your head, you can swap in LED lamps. See resulting page at bulbs.com for search "LED Light Bulbs with a G9 Base". Note that length and diameter need to be checked for compatibility. Also the dimmer vs. the bulb would need to be checked, or at least tested.

You also need a make-up air approach compatible with the blower size and the existence or not of combustion appliances taking air from any space common to the kitchen.

Thank you both for your help. I learned a lot.

"...you can swap in LED lamps"

Not necessarily. The dimmer may not support LEDs and/or LED bulbs may not support the very high temperatures they'd be subject to.

Has anyone found a solution to this problem?

Which problem? If the "high temperatures" problem, I don't think it applies to hoods. If the flow rate meets the requirements of the entry aperture (90 CFM/sq. ft.), temperatures at the hood margin or inside the hood are only a bit warmer than the ambient. Conceivably, with the hood off and all gas or coil electric burners on, the temperature of the rising air might be hot. The LED lamp's bases are to some extent heat-sunk into the hood structure, so even this condition seems safe enough for me, but I only have one hood, not a variety of them. One can easily test my intuition at modest cost.